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Vrite the complex number in trigonometric form r(cos 0 + i sin 0), with 0 in the interval [0°, 360°). 8) 53 + 5i

Vrite the complex number in trigonometric form r(cos 0 + i sin 0), with 0 in the interval [0°, 360°). 8) 53 + 5i

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Vrite the complex number in trigonometric form r(cos 0 + i sin 0), with 0 in the interval [0°, 360°). 8) 5 3 + 5i
Transcribed Image Text:Vrite the complex number in trigonometric form r(cos 0 + i sin 0), with 0 in the interval [0°, 360°). 8) 5 3 + 5i
Expert Solution
Step 1

Consider the given complex number: z=53+5i.

The trigonometric form of the complex number is rcosθ+isinθ.

Here, r is the modulus of the complex number and θ is called the argument of the complex number.

The formula for the modulus of any complex number a+bi is defined as,

r=a2+b2

Substitute a=53,b=5 in the formula for modulus.

r=532+52 =75+25 =100 =10

Since r is the modulus, it is always positive. So, r= 10.

 

 

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