# Solve Z^60

1. Jan 21, 2008

### nicksauce

1. The problem statement, all variables and given/known data
Evaluate $$z^{60}$$, where $$z = -1 + i\sqrt{3}$$

2. Relevant equations

3. The attempt at a solution
$$z = 2(\cos(\frac{2\pi}{3}) + i\sin(\frac{2\pi}{3})$$
$$z^{60} = 2^{60}(\cos(40\pi) + i\sin(40\pi))$$
$$z^{60} = 2^{60}$$

Is this right? Maple doesn't seem to agree.

2. Jan 21, 2008

### Mystic998

Unless I'm misremembering the various formulas involved, that seems correct. What is Maple giving as the answer?

3. Jan 21, 2008

### nicksauce

z := -1 + I sqrt(3)
a := z^60
evalf(a, 5)
1.1544 10^18 - 8.5175 10^14 I

Perhaps the imaginary part is just due to some kind of rounding error?

4. Jan 21, 2008

### Mystic998

Probably so. After all, you're dealing with some pretty big numbers and using, I'm guessing, 5 digits. Bound to introduce a pretty big error.

5. Jan 21, 2008

### nicksauce

I'm quite surprised maple wouldn't use exact methods, such as I used here, to calculate such numbers!