# The number 3 + 4 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 27E
To determine

## To write: The number 3+4i in polar form with argument between 0 and 2π.

Expert Solution

The number 3+4i written in polar form as 3+4i=5[cos(tan1(43))+isin(tan1(43))]

### 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+4i.

Obtain the argument of the complex number 3+4i.

tanθ=ba=43

Thus, the argument of argument of the complex number 3+4i is θ=tan1(43)

Obtain the modulus of the complex number 3+4i.

r=|3+4i|==32+42=25=5

Thus, the value of r=5.

Therefore, the polar form of the complex number 3+4i is 3+4i=5[cos(tan1(43))+isin(tan1(43))].

### 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!