# The number − 3 + 3 i in polar form with argument between 0 and 2 π .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter I, Problem 25E
To determine

## To write: The number −3+3i in polar form with argument between 0 and 2π.

Expert Solution

The number 3+3i written in polar form as 3+3i=32(cos3π4+isin3π4).

### Explanation of Solution

The polar form of the complex number z=a+bi is z=r(cosθ+isinθ) where r=|z|=a2+b2  and tanθ=ba.

Consider the complex number 3+3i.

Obtain the argument of the complex number 3+3i.

tanθ=ba=33=1

Thus, the argument of argument of the complex number 3+3i is θ=tan1(1)=3π4

Obtain the modulus of the complex number 3+3i.

r=|3+3i|==(3)2+32=18=32

Thus, the value of r=32.

Therefore, the polar form of the complex number 3+3i is 3+3i=32(cos3π4+isin3π4).

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