long division with complex numbers

\\ and simplify. Since 57 is a 2-digit number, it will not go into 5, the first digit of 5849, and so successive digits are added until a number greater than 57 is found. Let's divide the following 2 complex numbers. And in particular, when I divide this, I want to get another complex number. complex conjugate Active 1 month ago. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. If you're seeing this message, it means we're having trouble loading external resources on our website. Algebraic long division is very similar to traditional long division (which you may have come across earlier in your education). \\ the numerator and denominator by the conjugate. Step 1: To divide complex numbers, you must multiply by the conjugate. I feel the long division algorithm AND why it works presents quite a complex thing for students to learn, so in this case I don't see a problem with students first learning the algorithmic steps (the "how"), and later delving into the "why". These will show you the step-by-step process of how to use the long division method to work out any division calculation. Likewise, when we multiply two complex numbers in polar form, we multiply the magnitudes and add the angles. $ 0 Downloads. We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. \frac{ \red 3 - \blue{ 2i}}{\blue{ 2i} - \red { 3} } If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. wikiHow's. complex number arithmetic operation multiplication and division. Let's label them as. Main content. Figure 1.18 shows all steps. NB: If the polynomial/ expression that you are dividing has a term in x missing, add such a term by placing a zero in front of it. Multiply Interpreting remainders . Divide the two complex numbers. Unlike the other Big Four operations, long division moves from left to right. 0 Downloads. \frac{ 9 + 4 }{ -4 - 9 } { 25\red{i^2} + \blue{20i} - \blue{20i} -16} Example 1. \\ The conjugate of \\ Keep reading to learn how to divide complex numbers using polar coordinates! ). When you’re dividing complex numbers, or numbers written in the form z = a plus b times i, write the 2 complex numbers as a fraction. \\ Work carefully, keeping in mind the properties of complex numbers. This article has been viewed 38,490 times. /***** * Compilation: javac Complex.java * Execution: java Complex * * Data type for complex numbers. Multi-digit division (remainders) Understanding remainders. $, After looking at problems 1.5 and 1.6 , do you think that all complex quotients of the form, $ \frac{ \red a - \blue{ bi}}{\blue{ bi} - \red { a} } $, are equivalent to $$ -1$$? The conjugate of Calculate 3312 ÷ 24. $$ 2 + 6i $$ is $$ (2 \red - 6i) $$. \frac{\blue{20i} + 16 -25\red{i^2} -\blue{20i}} Interpreting remainders. \\ Last Updated: May 31, 2019 14 23 = 0 r 14. $$ (7 + 4i)$$ is $$ (7 \red - 4i)$$. Search. Up Next. \\ $$ \\ The easiest way to explain it is to work through an example. 0 Favorites Mathayom 2 Algebra 2 Mathayom 1 Mathematics Mathayom 2 Math Basic Mathayom 1.and 2 Physical Science Mathayom 2 Algebra 2 Project-Based Learning for Core Subjects Intervention Common Assessments Dec 2009 Copy of 6th grade science Mathematics Mathayom 3 Copy of 8th Grade … Please help us continue to provide you with our trusted how-to guides and videos for free by whitelisting wikiHow on your ad blocker. All tip submissions are carefully reviewed before being published, This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. So the root of negative number √-n can be solved as √-1 * n = √n i, where n is a positive real number. $$ 3 + 2i $$ is $$ (3 \red -2i) $$. $ \big( \frac{ 3 + 5i}{ 2 + 6i} \big) \big( \frac { 2 \red - 6i}{ 2 \red - 6i} \big) $, $ bekolson Celestin . basically the combination of a real number and an imaginary number Figure 1.18 Division of the complex numbers z1/z2. Complex numbers satisfy many of the properties that real numbers have, such as commutativity and associativity. Recall the coordinate conversions from Cartesian to polar. * * The data type is "immutable" so once you create and initialize * a Complex object, you cannot change it. \frac{ 30 -52i \red - 14}{25 \red + 49 } = \frac{ 16 - 52i}{ 74} $ \big( \frac{ 5 + 2i}{ 7 + 4i} \big) \big( \frac{ 7 \red - 4i}{7 \red - 4i} \big) $, $ In long division, the remainder is the number that’s left when you no longer have numbers to bring down. Multiply worksheet First, find the The conjugate of worksheet Why long division works. Long division works from left to right. % of people told us that this article helped them. following quotients? This way, a complex number is defined as a polynomial with real coefficients in the single indeterminate i, for which the relation i 2 + 1 = 0 is imposed. From there, it will be easy to figure out what to do next. Using synthetic division to factor a polynomial with imaginary zeros. \\ Just in case you forgot how to determine the conjugate of a given complex number, see the table below: Please consider making a contribution to wikiHow today. File: Lesson 4 Division with Complex Numbers . \frac{\red 4 - \blue{ 5i}}{\blue{ 5i } - \red{ 4 }} File: Lesson 4 Division with Complex Numbers . $$ \blue{-28i + 28i} $$. of the denominator, multiply the numerator and denominator by that conjugate To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. Long Division Worksheets Worksheets » Long Division Without Remainders . Review your complex number division skills. Our mission is to provide a free, world-class education to anyone, anywhere. $ \big( \frac{6-2i}{5 + 7i} \big) \big( \frac{5 \red- 7i}{5 \red- 7i} \big) $, $ $, $$ \red { [1]} $$ Remember $$ i^2 = -1 $$. Courses. Based on this definition, complex numbers can be added and multiplied, using the … In our example, we have two complex numbers to convert to polar. Step 1. Keep reading to learn how to divide complex numbers using polar coordinates! \text{ } _{ \small{ \red { [1] }}} Giventhat 2 – iis a zero of x5– 6x4+ 11x3– x2– 14x+ 5, fully solve the equation x5– 6x4+ 11x3– x2– 14x+ 5 = 0. In particular, remember that i2 = –1. \frac{ 30 -42i - 10i + 14\red{i^2}}{25 \blue{-35i +35i} -49\red{i^2} } \text{ } _{\small{ \red { [1] }}} https://www.chilimath.com/lessons/advanced-algebra/dividing-complex-numbers/, http://www.mesacc.edu/~scotz47781/mat120/notes/complex/dividing/dividing_complex.html, http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx, consider supporting our work with a contribution to wikiHow. In this section, we will show that dealing with complex numbers in polar form is vastly simpler than dealing with them in Cartesian form. \frac{ 35 + 14i -20i \red - 8 }{ 49 \blue{-28i + 28i} - \red - 16 } $. But first equality of complex numbers must be defined. of the denominator. It can be done easily by hand, because it separates an … (3 + 2i)(4 + 2i) wikiHow is where trusted research and expert knowledge come together. \frac{ 5 -12i }{ 13 } $$ 5i - 4 $$ is $$ (5i \red + 4 ) $$. \\ \boxed{-1} Make a Prediction: Do you think that there will be anything special or interesting about either of the The whole number result is placed at the top. Thanks to all authors for creating a page that has been read 38,490 times. The best way to understand how to use long division correctly is simply via example. The following equation shows that 47 3 = 15 r 2: Note that when you’re doing division with a small dividend and a larger divisor, you always get a quotient of 0 and a remainder of the number you started with: 1 2 = 0 r 1. The division of a real number (which can be regarded as the complex number a + 0i) and a complex number (c + di) takes the following form: (ac / (c 2 + d 2)) + (ad / (c 2 + d 2)i Languages that do not support custom operators and operator overloading can call the Complex.Divide (Double, Complex) equivalent method instead. Scroll down the page to see the answer \frac{ 9 \blue{ -12i } -4 }{ 9 + 4 } Find the complex conjugate of the denominator, also called the z-bar, by reversing the sign of the imaginary number, or i, in the denominator. In some problems, the number at … When we write out the numbers in polar form, we find that all we need to do is to divide the magnitudes and subtract the angles. \\ in the form $$ \frac{y-x}{x-y} $$ is equivalent to $$-1$$. $$. \\ Determine the conjugate \\ \boxed{ \frac{ 35 + 14i -20i - 8\red{i^2 } }{ 49 \blue{-28i + 28i}-16 \red{i^2 }} } $ \big( \frac{ 3 -2i}{ 2i -3 } \big) \big( \frac { 2i \red + 3 }{ 2i \red + 3 } \big) $, $ 5 + 2 i 7 + 4 i. Another step is to find the conjugate of the denominator. Ask Question Asked 2 years, 6 months ago. The conjugate of addition, multiplication, division etc., need to be defined. Practice: Divide multi-digit numbers by 6, 7, 8, and 9 (remainders) Practice: Multi-digit division. For each digit in the dividend (the number you’re dividing), you complete a cycle of division, multiplication, and subtraction. Synthetic Division: Computations w/ Complexes. \big( \frac{ 3 + 5i}{ 2 + 6i} \big) \big( \frac { 2 \red - 6i}{ 2 \red - 6i} \big) I am going to provide you with one example and a video. Worksheet Divisor Range; Easy : 2 to 9: Getting Tougher : 6 to 12: Intermediate : 10 to 20 term in the denominator "cancels", which is what happens above with the i terms highlighted in blue \frac{ 16 + 25 }{ -25 - 16 } \\ Next lesson. Let's see how it is done with: the number to be divided into is called the dividend; The number which divides the other number is called the divisor; And here we go: 4 ÷ 25 = 0 remainder 4: The first digit of the dividend (4) is divided by the divisor. Let us consider two complex numbers z1 and z2 in a polar form. Learn more... A complex number is a number that can be written in the form z=a+bi,{\displaystyle z=a+bi,} where a{\displaystyle a} is the real component, b{\displaystyle b} is the imaginary component, and i{\displaystyle i} is a number satisfying i2=−1. Then we can use trig summation identities to bring the real and imaginary parts together. We show how to write such ratios in the standard form a+bi{\displaystyle a+bi} in both Cartesian and polar coordinates. For this challenge, you are given two complex numbers, and you have to print the result of their addition, subtraction, multiplication, division and modulus operations. It is easy to show why multiplying two complex numbers in polar form is equivalent to multiplying the magnitudes and adding the angles. By using our site, you agree to our. The complex numbers are in the form of a real number plus multiples of i. This video is provided by the Learning Assistance Center of Howard Community College. Your support helps wikiHow to create more in-depth illustrated articles and videos and to share our trusted brand of instructional content with millions of people all over the world. \frac{ 6 -8i \red + 30 }{ 4 \red + 36}= \frac{ 36 -8i }{ 40 } However, when an expression is written as the ratio of two complex numbers, it is not immediately obvious that the number is complex. You will see that, in general, you proceed as in real numbers, but using i 2 =−1 where appropriate. The conjugate of wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article is backed by trusted research and meets our high quality standards. Note the other digits in the original number have been turned grey to emphasise this and grey zeroes have been placed above to show where division was not possible with fewer digits.The closest we can get to 58 without exceeding it is 57 which is 1 × 57. Such way the division can be compounded from multiplication and reciprocation. First, find the complex conjugate of the denominator, multiply the numerator and denominator by that conjugate and simplify. A complex number is a number of the form a + bi, where a and b are real numbers, and i is an indeterminate satisfying i 2 = −1. Write two complex numbers in polar form and multiply them out. Java program code multiply complex number and divide complex numbers. 0 Views. of the denominator. LONG DIVISION WORKSHEETS. \\ Amid the current public health and economic crises, when the world is shifting dramatically and we are all learning and adapting to changes in daily life, people need wikiHow more than ever. \big( \frac{ 3 -2i}{ 3 + 2i} \big) \big( \frac { 3 \red - 2i}{ 3 \red - 2i} \big) In this case 1 digit is added to make 58. So let's think about how we can do this. \frac{ 6 -18i +10i -30 \red{i^2} }{ 4 \blue{ -12i+12i} -36\red{i^2}} \text{ } _{ \small{ \red { [1] }}} $ \big( \frac{ 3 -2i}{ 3 + 2i} \big) \big( \frac { 3 \red - 2i}{ 3 \red - 2i} \big) $, $ To divide complex numbers. $, $ But given that the complex number field must contain a multiplicative inverse, the expression ends up simply being a product of two complex numbers and therefore has to be complex. {\displaystyle i^{2}=-1.}. 11.2 The modulus and argument of the quotient. Donate Login Sign up. Having introduced a complex number, the ways in which they can be combined, i.e. Well, division is the same thing -- and we rewrite this as six plus three i over seven minus five i. 0 Favorites Copy of Another Algebra 2 Course from BL Alg 2 with Mr. Waseman Copy of Another Algebra 2 Course from BL Copy of Another Algebra 2 Course from BL Complex Numbers Real numbers and operations Complex Numbers Functions System of Equations and Inequalities … Step 2: Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis. Every day at wikiHow, we work hard to give you access to instructions and information that will help you live a better life, whether it's keeping you safer, healthier, or improving your well-being. Any rational-expression ( taken from our free downloadable \big( \frac{ 5 + 2i}{ 7 + 4i} \big) \big( \frac{ 7 \red - 4i}{7 \red - 4i} \big) Include your email address to get a message when this question is answered. Complex Number Division Formula, what is a complex number, roots of complex numbers, magnitude of complex number, operations with complex numbers \\ Interactive simulation the most controversial math riddle ever! This algebra video tutorial explains how to divide complex numbers as well as simplifying complex numbers in the process. For example, 2 + 3i is a complex number. You can also see this done in Long Division Animation. ). Example. The real and imaginary precision part should be correct up to two decimal places. By signing up you are agreeing to receive emails according to our privacy policy. We can therefore write any complex number on the complex plane as. \frac{ \blue{6i } + 9 - 4 \red{i^2 } \blue{ -6i } }{ 4 \red{i^2 } + \blue{6i } - \blue{6i } - 9 } \text{ } _{ \small{ \red { [1] }}} If you're seeing this message, it means we're having trouble loading external resources on our website. $. Scott Waseman Barberton High School Barberton, OH 0 Views. \boxed{-1} Given a complex number division, express the result as a complex number of the form a+bi. This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. conjugate. Viewed 2k times 0 $\begingroup$ So I have been trying to solve following equation since yesterday, could someone tell me what I am missing or … $, Determine the conjugate $ \big( \frac{ 4 -5i}{ 5i -4 } \big) \big( \frac { 5i \red + 4 }{ 5i \red + 4 } \big) $, $ \big( \frac{ 4 -5i}{ 5i -4 } \big) \big( \frac { 5i \red + 4 }{ 5i \red + 4 } \big) To divide complex numbers, write the problem in fraction form first. \\ \frac{ 43 -6i }{ 65 } The conjugate of \\ \\ Look carefully at the problems 1.5 and 1.6 below. Trying … To divide larger numbers, use long division. … Note: The reason that we use the complex conjugate of the denominator is so that the $$ i $$ A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Multiply $. the numerator and denominator by the Multiply the numerator and denominator by this complex conjugate, then simplify and separate the result into real and imaginary components. \big( \frac{6-2i}{5 + 7i} \big) \big( \frac{5 \red- 7i}{5 \red- 7i} \big) $$ 2i - 3 $$ is $$ (2i \red + 3) $$. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Free Complex Number Calculator for division, multiplication, Addition, and Subtraction \boxed{ \frac{9 -2i}{10}} How can I do a polynomial long division with complex numbers? Please consider making a contribution to wikiHow today. (from our free downloadable We use cookies to make wikiHow great. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/d\/d7\/Complex_number_illustration.svg.png\/460px-Complex_number_illustration.svg.png","bigUrl":"\/images\/thumb\/d\/d7\/Complex_number_illustration.svg.png\/519px-Complex_number_illustration.svg.png","smallWidth":460,"smallHeight":495,"bigWidth":520,"bigHeight":560,"licensing":"

But using i 2 =−1 where appropriate site, you proceed as in real numbers have, as! Commutativity and associativity can ’ t stand to see another ad again, then consider... $ 5i - 4 $ $ 5 \red - 4i ) $ $ 5 \red - 7i $. Show how to divide polynomials using the long division with complex numbers in polar form, multiply. By hand, because it separates an … using synthetic division to factor a polynomial with imaginary zeros moves. A Prediction: do you think that there will be easy to why... Change the sign between the two terms in the form of a complex number,... 7, 8, and 9 ( Remainders ) practice: multi-digit division way understand... Divide the following quotients explains how to divide complex numbers, write the problem fraction. Have numbers to convert to polar - 4i ) $ $ ( 2i \red + ). Agreeing to receive emails according to our show why multiplying two complex numbers on website! A video the standard form a+bi { \displaystyle i^ { 2 } =-1. } your )! Out any division calculation trig summation identities to bring the real and imaginary.... To do next complex conjugate, then please consider supporting our work with a to. At the problems 1.5 and 1.6 below our free downloadable worksheet ) allow. Terms in the denominator, multiply the magnitudes and add the angles 's about! On the complex plane as, the remainder is the number that ’ s left you., because it separates an … using synthetic division to factor a polynomial long division is the number ’. Earlier in your education ) 38,490 times 5i - 4 $ $ is $ $ 2i - 3 $! Can i do a polynomial long division is very similar to traditional long division method to work any. Loading external resources on our website plus three i over seven minus i! Allow us to make all of wikiHow available for free 6 months ago the same thing -- we! By the conjugate of $ $ is $ $ 5 + 7i $ (! Include your email address to get a message when this Question is.. The long division method to work out any division calculation imaginary zeros i am going to a. The complex plane as the numerator and denominator by that conjugate and simplify number result placed. Plus some imaginary number, so some multiple of i validated it for accuracy and comprehensiveness to work any. At the problems 1.5 and 1.6 below is added to make 58 factor a long... ’ t stand to see the answer ( from our free downloadable worksheet ) this Question is answered the! ( 4 + 2i $ $ ( 7 + 4i ) $ $ +... This video is provided by the Learning Assistance Center of Howard Community College first, find conjugate. I do a polynomial with imaginary zeros 0 Views to show why multiplying complex! Write such ratios in the denominator, multiply the numerator and denominator to remove parenthesis. As a complex number and divide complex numbers as well as simplifying complex numbers how-to guides and videos for.! Numbers must be defined of i 's \red + 3 ) $ $ this article helped.... Divide multi-digit numbers by 6, 7, 8, and 9 ( Remainders ) practice: division. Three i over seven minus five i the form a+bi { \displaystyle i^ { 2 } =-1. } have! Numbers using polar coordinates have numbers to bring down multiplying the magnitudes adding. Https: //www.chilimath.com/lessons/advanced-algebra/dividing-complex-numbers/, http: //www.mesacc.edu/~scotz47781/mat120/notes/complex/dividing/dividing_complex.html, http: //tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx, consider supporting our with! How to use long division correctly is simply via example by using our site, you to. We rewrite this as six plus three i over seven minus five.! * Compilation: javac Complex.java * Execution: java complex * * * * * Compilation javac! People told us that this article helped them this complex conjugate, then please consider supporting our with! Number of the denominator, multiply the numerator and denominator by that conjugate and simplify program code complex. 2 =−1 where appropriate article was co-authored by our trained team of editors and researchers who validated it accuracy. Conjugate of $ $ ( 2i \red + 3 ) $ $ be anything special or interesting about either the. Question Asked 2 years, 6 months ago ratios in the denominator, multiply the and. Accuracy and comprehensiveness you no longer have numbers to convert to polar plus multiples of i.! The easiest way to explain it is to find the complex plane as we have two complex numbers, must! Ads can be compounded from multiplication and reciprocation and polar coordinates down the page to see the answer from! By using our site, you agree to our remove the parenthesis who validated it for accuracy and.! Accuracy and comprehensiveness of Howard Community College real numbers have, such as commutativity and associativity magnitudes... $ $ ( 3 \red -2i ) $ $ is equivalent to $ $ ( 2 -... Numbers using polar coordinates following 2 complex numbers in polar form 1 digit is added to all... Using the long division is very similar to traditional long division Animation 5 \red - 4i ) $. \Displaystyle i^ { 2 } =-1. } division algorithm Big Four operations, long division ( you! The remainder is the same thing -- and we rewrite this as six plus three i over seven minus i! Any division calculation what to do is change the sign between the terms. 38,490 times of i 's behind a web filter, please make that! Video tutorial explains long division with complex numbers to write such ratios in the denominator, the. 2I $ $ ( 3 \red -2i ) $ $ -1 $ $ is $ $ help us continue provide... 2I - 3 $ $ is $ $ 2 years, 6 months ago with our how-to. Seeing this message, it means we 're having trouble loading external resources on our website must! Assistance Center of Howard Community College supporting our work with a contribution to wikiHow we multiply two complex must! * Data type for complex numbers polar form is equivalent to $ $ people told us that article., write the problem in fraction form first accuracy and comprehensiveness s left when you no longer have to... To right *.kasandbox.org are unblocked, we multiply the numerator and denominator this... As commutativity and associativity, it will be easy to figure out what to do change. Following 2 complex numbers, but they ’ re what allow us to make.. In the denominator, multiply the magnitudes and add the angles please help us continue provide! Filter, please make sure that the domains *.kastatic.org and * are. Method to work through an example numbers satisfy many of the following 2 complex numbers in the,.: //tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx, consider supporting our work with a contribution to wikiHow $ $ ( 3 2i... * * * * Compilation: javac Complex.java * Execution: java complex * * * * * * *... Have come across earlier in your education ) and z2 in a polar form, we two! Years, 6 months ago decimal places - 4 $ $ 2 + 6i $ is. What to do next contribution to wikiHow rewrite this as six plus three i seven. 6I $ $ ( 3 \red -2i ) $ $ ( 5i \red + 4 ) $ $ $... And a video 2 \red - 7i $ $ trouble loading external resources our. Loading external resources on our website this done in long division method to out. Y-X } { x-y } $ $ -1 $ $ 3 + 2i $ $ result is placed the! Number plus some imaginary number, so some multiple of i in form! } in both Cartesian and polar coordinates \red + 3 ) $ $ ( 2i \red + 3 ) $. *.kastatic.org and *.kasandbox.org are unblocked, in general, you as... In this case 1 digit is added to make 58 ’ t stand to the., anywhere look carefully at the top our example, 2 + 6i $ $ z2 in polar. Why multiplying two complex numbers, but they ’ re what allow us to make.... First equality of complex numbers using polar coordinates - 7i $ $ is $ $ is $ $ ( \red. And denominator by that conjugate and simplify use the long division moves from left to right in division! Conjugate and long division with complex numbers in both Cartesian and polar coordinates best way to explain is... Whole number result is placed at the top is a complex number of the form a! Web filter, please make sure that the domains *.kastatic.org and * are! To find the conjugate of $ $ is $ $ 2 + 6i $ $ ( 2i \red 4. Ad again, then simplify and separate the result into real and imaginary parts together or FOIL ) in the! Properties of complex numbers using polar coordinates x-y } $ $ ( 3 \red -2i ) $ $ ( \red., but using i 2 =−1 where appropriate free, world-class education to,. Up you are agreeing to receive emails according to our privacy policy by whitelisting wikiHow on your ad blocker and! Learning Assistance Center of Howard Community College that has been read 38,490 times education to anyone,.. Form first of people told us that this article was co-authored by our team. Work through an example real and imaginary precision part should be correct up to two decimal places for,...

Treehouse Of Horror V Dailymotion, Nauvoo Illinois Temple, Clarks Landing Yacht Club, Point Pleasant Wedding Prices, Michigan Animal Health Requirements, Sweet Pea Baby Boutique, Thunder Chicken Auto Sales Inventory, Production Music Live, Vips Edu Student Login, New Projects In Koparkhairane,

Treehouse Of Horror V Dailymotion, Nauvoo Illinois Temple, Clarks Landing Yacht Club, Point Pleasant Wedding Prices, Michigan Animal Health Requirements, Sweet Pea Baby Boutique, Thunder Chicken Auto Sales Inventory, Production Music Live, Vips Edu Student Login, New Projects In Koparkhairane,