De moivres theorem

Question

Perform the indicatd operation using De Moivres theorem. Note your answer must be a single complex number in a+bi form. (-5+4i)^3

Answer 1

Step 1:

De Moivres Theorem:

If is a complex number, then

where is a positive integer.

Step 2:

The complex number is .

The complex number .

Write the complex number in polar form.

The argument is .

Polar form of is .

De Moivres theorem: .

Then, raise the complex number to given power.

Solution: