solutions of a complex number equation

[M-D]

Hi,

i need to find the roots for z^5=32i only in exponential form. Here are the ones i got:

2e^i*pi/10
2e^i*pi/2
2e^i*9pi/10
2e^i*13pi/10=2e^-i*7pi/10 (principal argument)
2e^i*17pi/10=2e^-i3pi/10 (principal argument)
 
are they correct. I appreciate your help

[Alwin]

Hi,

i need to find the roots for z^5=32i only in exponential form. Here are the ones i got:

2e^i*pi/10
2e^i*pi/2
2e^i*9pi/10
2e^i*13pi/10=2e^-i*7pi/10 (principal argument)
2e^i*17pi/10=2e^-i3pi/10 (principal argument)
 
are they correct. I appreciate your help

Yes, that's correct.

[lzxnl]

Well as an easy check if your solution makes sense, check the magnitudes of both sides. Here, |z|=2 as you can tell. Next, confirm that one of your answers is correct. In this case, we'll check that 2e^(i*pi/2) is correct, and it is, as that is 2i and (2i)^5 is clearly 32i. Finally, check that the arguments of all of your answers are spaced out evenly by 2pi/n. You can check this one.