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Chapter 7: Q1E (page 371)

Write the complex number Z = 3 - 3iin polar form.

Short Answer

Expert verified

The polar form of the complex number isz=32fcos-蟺4+isin-蟺4

Step by step solution

01

Definition

A complex number is one of the form a + bi, where a and b are real numbers. a is called the real part of the complex number, and b is called the imaginary part. Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.

The polar form of a complex number is a different way to represent a complex number apart from rectangular form. Usually, we represent the complex numbers, in the form of z = x+iy where 'i' the imaginary number. But in polar form, the complex numbers are represented as the combination of modulus and argument.

02

Step 2: polar form

We have,

z=32+32=32

tan蠁=33=-1蠁=蟺4

Therefore,

z=32fcos-蟺4+isin-蟺4

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