BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 28E

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).

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!