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Chapter 7: Problem 97

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

Short Answer

Expert verified
To convert a complex number from polar to rectangular form, apply the equations \( x = r \cos \theta \) and \( y = r \sin \theta \) to find the real part \( x \) and the imaginary part \( y \) respectively. Then, express the complex number in rectangular form as \( z = x + iy \).

Step by step solution

01

Identify the polar form of the complex number

The polar form of a complex number is typically given as \( r \angle \theta \). The complex number is represented by the magnitude \( r \) and the angle \( \theta \) in degrees or radians.
02

Transform the polar form to rectangular form

To obtain the rectangular form \( z = x + iy \), apply the equations \( x = r \cos \theta \) and \( y = r \sin \theta \). The real part \( x \) is found by multiplying the magnitude \( r \) by the cosine of the angle \( \theta \). Similarly, the imaginary part \( y \) is found by multiplying the magnitude \( r \) by the sine of the angle \( \theta \). Note that \(\cos \theta \) points to the real part and \(\sin \theta \) points to the imaginary part.
03

Write the rectangular form

After calculating \( x \) and \( y \), express the complex number in rectangular form as \( z = x + iy \). Note that \( i \) represents the imaginary unit.

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Most popular questions from this chapter

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