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Chapter 6: Problem 97

If you are given a complex number in polar form, how do you write it in rectangular form?

Short Answer

Expert verified
A complex number in polar form is converted to rectangular form by utilizing the components \(r\) (the modulus) and \(\theta\) (the argument). The real part \(a\) is \(r \cos{\theta}\) and the imaginary part \(b\) is \(r \sin{\theta}\). Thus, the rectangular form of the complex number will be \(a + bi\).

Step by step solution

01

Identify \(r\) and \(\theta\)

To start, one needs to identify the values of \(r\) (the modulus) and \(\theta\) (the argument) within the given complex number.
02

Convert to Rectangular Form

Next, convert the polar form to rectangular form. The real part, \(a\), of the complex number in rectangular form is calculated by multiplying the modulus \(r\) by the cosine of the argument \(\theta\), i.e., \(a = r \cos{\theta}\). The imaginary part, \(b\), is calculated as \(b = r \sin{\theta}\). This provides the complex number in rectangular form as \(a + bi\).
03

Simplify if needed

The results from Step 2 are usually sufficient. However, sometimes one might have to simplify further, if possible, to give the simplest form of the complex number.

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Most popular questions from this chapter

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