(a)

how do you find the fifth root of -16 ( 2) ^ (1/2) ( 1+i)

What did you write here? Is it ?
i found that the mod of z^5 is 4. and the argument of ( 1+i ) = (Pi /2)

This is wrong if the number is what I wrote above: if , then Also, its argument is So try now to solve your question with the above info...and check how come you thought it was something else!

Tonio
from there, i said that the arg of z is ( Pi / 10 + 2k Pi / 5)

thus the answer for the fifth root of z would be of the form,

z = 4 (cos ( Pi / 10 + 2k Pi / 5) + i sin (Pi / 10 + 2k Pi / 5) )

am i right to say that?

(b)

also is there a fixed method that i can do to compute questions like ( 1-i) ^ ( -3) and ( -1 + i) ^16?

becos

Oh, and please: it is "because"...common, a little university level's basic writing.
now im just doing them via expansion and im wondering if there is a shorter method that i can do to solve it..

thanks!