# Calculating complex number

1. May 19, 2008

### Theofilius

[SOLVED] calculating complex number

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

Calculate $${i}^{\frac{3}{4}}$$

2. Relevant equations

3. The attempt at a solution

I tried with

$$i=cos\frac{pi}{2}+isin\frac{\pi}{2}$$

$$i^3=cos\frac{3pi}{2}+isin\frac{3\pi}{2}$$

$$i^3=-i$$

$$\sqrt[4]{i^3}=\sqrt[4]{-i}$$

I don't know where I should go out of here. Please help!

2. May 19, 2008

### Dick

Why don't you just go all the way at once? i=e^(i*pi/2). So i^(-3/4)=(e^(i*pi/2))^(-3/4). Now use laws of exponents. Notice this answer isn't unique. i is also equal to e^(i*(pi/2+2pi)=e^(i*5pi/2). This is the same sort of nonuniqueness you get with square roots.

3. May 20, 2008

### Theofilius

Thanks. I solve it.