w=5(cos(pi/12)+i sin(pi/12) is one of six roots of complex number z. what are the other 5 roots (in trigometric form) and z?

Question

sirm3d · Answer

Hint: the six sixth roots of a complex number z are equally spaced about the circle of radius $$\Large \sqrt[6]{|z|}$$|dw:1360979026730:dw|

anonymous · Answer

i need a little more help. i see where you are going, but im not sure what is next.

anonymous · Answer

do exactly what @sirm3d said.
divide the circle up in to 6 equal parts, with one of them at $\frac{\pi}{12}$

anonymous · Answer

sorry, but im still lost.

anonymous · Answer

ok, i have the other roots, now how do i use them to find z?

anonymous · Answer

is the answer z=15625i?

anonymous · Answer

To solve this, you'd need to be able to understand De Moivre's theorem on finding n-th roots of complex numbers. Wikipedia can certainly help. http://en.wikipedia.org/wiki/De_Moivre's_formula Put it into De Moivre's equation form.

anonymous · Answer

can you check my answer?