# Little confused about raising a complex number to a power.

1. Jun 12, 2012

### charmedbeauty

1. The problem statement, all variables and given/known data

α=2e3∏i/4

find α11 in cartesian form.

2. Relevant equations

3. The attempt at a solution

It's been a while since I've done these but from what remember you add 2kpi to get exp in the range of -∏,∏.

so if I let k=15

I get e3∏i/4

but the sltn says it needs to be raised to ∏i/4

can some one please tell me why, should I be adding 4k∏ since it is divided by 4?

Thanks.

2. Jun 12, 2012

### HallsofIvy

Staff Emeritus
Oh, dear! I just divided wrong! 33/7= 8+ 1/7.

Last edited: Jun 12, 2012
3. Jun 12, 2012

### clamtrox

I get something different.. $(e^{3 \pi i /4} )^{11} = e^{33 \pi i /4} = e^{8 \pi i + \pi i/4} = e^{\pi i/4}$

4. Jun 12, 2012

### Infinitum

Hmm, I get the exponent as $\pi i/4$.

We have,

$$\vec{p} = e^{3\pi i/4}$$

Raising the power to 11,

$$\vec{t} = e^{33\pi i/4}$$

Looking at $33\pi /4$ we see that it crosses the first quadrant$(2n\pi)$, 4 times, so that gives an angular displacement of $8\pi$. Let x be the angle in cartesian range we are looking for,

$$8\pi + x = \frac{33\pi}{4}$$

Edit : Just saw your edit :tongue2:

5. Jun 12, 2012

### charmedbeauty

oops I did the same thing, oh damn!

Thanks for clearing that up anyhow.