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Chapter 6: Problem 95

What is the polar form of a complex number?

Short Answer

Expert verified
The polar form of a complex number is \(z = r(\cos(胃) + i\sin(胃))\), where \(r = \sqrt{x^2 + y^2}\) is the magnitude or modulus and \(胃 = atan2(y, x)\) is the angle or argument.

Step by step solution

01

Define the complex number

Let's say the complex number is \(z = x + yi\), where \(x\) is the real part and \(y\) is the imaginary part of the complex number \(z\).
02

Calculate the magnitude (r)

The magnitude of the complex number, represented as \(r\), is calculated as the square root of the sum of the squares of the real and imaginary parts. In mathematical form, it is \(r = \sqrt{x^2 + y^2}\).
03

Calculate the angle (胃)

The angle \(胃\) that the complex number makes with the real axis is calculated using the tangent inverse (atan2) function. It is given by \(胃 = atan2(y, x)\).
04

Formulate into Polar Form

The complex number can now be represented in polar form as \(z = r(\cos(胃) + i\sin(胃))\).

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