Find the four fourth roots of z = 16( cos +i sin 12). Write each root in standard form. Wo = W1 = W2 = W3 =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 48E
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help me please 

Find the four fourth roots of z = 16( cos
+ i sin
Write each root in standard form.
Wo =
W1 =
W2 =
W3
Transcribed Image Text:Find the four fourth roots of z = 16( cos + i sin Write each root in standard form. Wo = W1 = W2 = W3
Expert Solution
Step 1

z=16cos2π3+isin2π3

For forth roots of z

z14=16cos2π3+isin2π314

z=2cos2+nπ3+isin2+nπ3 Where n=0,1,2,3

z= z=2cos2π3+isin2π3  Where n =0

for n=1 ,  z =2cos3π3+isin3π3

for n=2,  z=2cos4π3+isin4π3

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