The number 1 − 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 26E
To determine

To write: The number 1−3i in polar form with argument between 0 and 2π.

Expert Solution

The number 13i written in polar form as 13i=2(cos5π3+isin5π3).

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 13i.

Obtain the argument of the complex number 13i.

tanθ=ba=31=3

Thus, the argument of argument of the complex number 13i is θ=tan1(3)=5π3

Obtain the modulus of the complex number 13i.

r=|13i|==12+(3)2=1+3=2

Thus, the value of r=2.

Therefore, the polar form of the complex number 13i is 13i=2(cos5π3+isin5π3).

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