Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

De Moivre's Theorem is used to compute the powers and roots of a complex number. The formula is:

To be able to apply it, convert the complex number z=-1+i to trigonometric form.Take note that that the trigonometric form of

is

where

   and    

Applying these two formulas, the values of r and theta of z=-1+i are:

Since x is negative and y is positive, theta is located at the second quadrant. So the equivalent positive angle of theta is:

Then, plug-in the values of r and theta to the trigonometric form

Now that z=-1+i is in trigonometric form, proceed to compute z^6 .

     

     

     

     

     

Therefore,   .