Thread: Solving a power of a complex number

I have this problem:

x^4=4-4*(square root 3i)

I rewrote in trig form:

8cos300+isin300 then i solved by raising the 8^4 and multiplying the angle by 4...

The answer i got was 1499i. Could anyone verify my work for me? Is it correct to leave the imaginary "i" in the answer?

Originally Posted by nascar77

I have this problem:

x^4=4-4*(square root 3i)

I rewrote in trig form:

8cos300+isin300 then i solved by raising the 8^4 and multiplying the angle by 4...

The answer i got was 1499i. Could anyone verify my work for me? Is it correct to leave the imaginary "i" in the answer?

There are four solutions, found by raising to the power of 1/4, where n is an integer. Using four consecutive values of n (such as n = 0, 1, 2 and 3) after doing this will give you the four solutions.