Question

Which of the following is a third root of the given complex number?

27(cos(pi/5)+isin(pi/5))

Check all that apply.
A. 3(cos(8pi/15)+isin(8pi/15))
B. 3(cos(11pi/15)+isin(11pi/15))
C. 27(cos(11pi/15)+isin(11pi/15))
D. 3(cos(pi/15)+isin(pi/15))

Answer 1

27(cos(pi/5)+isin(pi/5))^1/3


hint :use this identity
\(( r (\cos \theta+i \sin \theta ))^n= r^n (\cos n\theta+i \sin n\theta ) \)

Answer 2

27^1/3(cos(pi/5)+isin(pi/5))^1/3 = 27^1/3 (cos(pi/15)+isin(pi/15) )
=3 (cos(pi/15)+isin(pi/15) )

Answer 3

got it ?
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