SOLUTION: Find the complex cube roots of 343(cos 291° + i sin 291°) A. -7(cos 97° + i sin 97°), 7(cos 137° + i sin 137°), -7(cos 177° + i sin 177°) B. 7(cos 97° - i sin 97°), 7(cos21

Algebra ->  Trigonometry-basics -> SOLUTION: Find the complex cube roots of 343(cos 291° + i sin 291°) A. -7(cos 97° + i sin 97°), 7(cos 137° + i sin 137°), -7(cos 177° + i sin 177°) B. 7(cos 97° - i sin 97°), 7(cos21      Log On


   



Question 978131: Find the complex cube roots of 343(cos 291° + i sin 291°)
A.
-7(cos 97° + i sin 97°), 7(cos 137° + i sin 137°), -7(cos 177° + i sin 177°)
B.
7(cos 97° - i sin 97°), 7(cos217° - i sin 217°), 7(cos 337° - i sin 337°)
C.
7(cos 97° + i sin 97°), 7(cos 137° + i sin 137°), 7(cos 177° + i sin 177°)
D.
7(cos 97° + i sin 97°), 7(cos217° + i sin 217°), 7(cos 337° + i sin 337°)
E.
-7(cos 97° + i sin 97°), 7(cos 217° + i sin 217°), -7(cos 337° + i sin 337°)

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the complex number r%28cos%28theta%29%2Bi%2Asin%28theta%29%29 ,
with r%3E=0 and 0%5Eo%3C=theta%3C360%5Eo ,
is the complex cube root of 343%28cos%28291%5Eo%29%2Bi%2Asin%28291%5Eo%29%29 , then
for system%28n=0%2Cn=1%2C%22or%22%2Cn=2%29 .
For that it must be
r%5E3=343--->r=7 and
3theta=291%5Eo%2Bn%2A360%5Eo for system%28n=0%2Cn=1%2C%22or%22%2Cn=2%29
Dividing both sides of the equation by 3 we get
3theta%2F3=%28291%5Eo%2Bn%2A360%5Eo%29%2F3
theta=291%5Eo%2F3%2Bn%2A360%5Eo%2F3
theta=97%5Eo%2Bn%2A120%5Eo--->