# The number 8 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 28E
To determine

## To write: The number 8i in polar form with argument between 0 and 2π.

Expert Solution

The number 8i written in polar form as 8i=8(cosπ2+isinπ2).

### 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 8i.

Obtain the argument of the complex number 8i.

tanθ=ba=80=

Thus, the argument of argument of the complex number 8i is θ=tan1()=π2

Obtain the modulus of the complex number 8i.

r=|8i|==(0)2+82=64=8

Thus, the value of r=8.

Therefore, the polar form of the complex number 8i is 8i=8(cosπ2+isinπ2).

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