# Solving a power of a complex number

• November 2nd 2009, 08:20 AM
nascar77
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?
• November 2nd 2009, 03:44 PM
mr fantastic
Quote:

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 $8 \cos (300 + 360n) + i \sin (300 + 360n)$ 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.