Compute z^5

Question

if z= 4 +3i?

Answer 1

Step 1:

The complex .

De Moivres theorem :

if is a complex number, then ,

where    and 

Consider .

Polar form of complex number is in the form of .

Step 2 :

Find .

Apply De Moivres theorem.

Substitute and .

.

.

Solution :

.