Question

which of the following are 5th roots of the complex number 32(cos(pi/3) +isin(pi/3))?
a. 32(cos(pi/15) +isin(pi/15))
b. 2(cos(7pi/15) +isin(7pi/15))
c. 2(cos(11pi/15) +isin(11pi/15))
d. 2(cos(pi/15) +isin(pi/15))

check all that apply

@mustafa2014

Answer 1

@linn99123
@undeadknight26

Answer 2

didn't learn this yet so sorry.

Answer 3

@phi

Answer 4

first, you want the 5th root of 32. any idea what that is ?

Answer 5

2^5 = 32 so you want a 2
out front

the 5th root of cos(x) + i sin(x) is cos(x/5) + i sin(x/5)
also, there are 5 roots located at even intervals around the circle. they are spaced every 2 pi/5 or 6 pi/15 radians

Answer 6

@phi what about the 3rd root of 27 (cos(pi/5) + isin(pi/5))?

i know 3 goes out front but i dont know the rest

Answer 7

divide the angle by 3 to pi/15

there are 3 roots, space 2pi/3 radians or 10 pi/15
so the roots are at pi/15, pi/15+ 10pi/15 = 11 pi/15
and pi/15+ 20pi/15 = 21 pi/15 (or 7 pi /5 )

Answer 8

thank you so much!!!!!!!!

Answer 9

yw