an important corollary to the euler identity i DeMoivre's Theorem, which finds the powers and roots of any complex number.
let z=x + iy be a complex number, which we associate with point (x,y) in the plane.
using polar coordinates we write z = r(cos theta + i sin theta) = re^i (theta), so that z^m = r e^ (i m theta) = r^m (cos m theta + i sin m theta)

(i) z = 1 + i and m = 10 then,
(ii) find all six of the roots to x^6 - 1 = 0

Question

an important corollary to the euler identity i DeMoivre's Theorem, which finds the powers and roots of any complex number. 
let z=x + iy be a complex number, which we associate with point (x,y) in the plane.
using polar coordinates we write z = r(cos theta + i sin theta) = re^i (theta), so that z^m = r e^ (i m theta) = r^m (cos m theta + i sin m theta)

(i) z = 1 + i and m = 10 then,
(ii) find all six of the roots to x^6 - 1 = 0

anonymous · Answer

$$z= r\cos\theta + r\sin\theta i = 1 +i\
r\cos\theta=1\
r\sin\theta=1\
r=?\
\theta=?
$$
Can you solve this part to find z polar coordinates?

sswann222 · Answer

|dw:1370278151466:dw|

we have tried and don't seem to be able to get very far. This is the figure that goes along with it.

sswann222 · Answer

i also know that DeMoivre's therem 

$$(\cos 10\theta + i \sin 10\theta) can be written as (\cos \theta + i \sin \theta) ^ 10$$