# Solve the Complex Numbers equation

1. Oct 21, 2014

### TheRedDevil18

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

Solve the following complex equation for z:

zi = sqrt(3) - i

2. Relevant equations

3. The attempt at a solution

Do I have to equate the real and imaginary parts ?, this is what I tried

zi = (x+iy)i = exp(i*log(x+iy))

2. Oct 21, 2014

### ehild

I suggest to use the exponential form.

ehild

3. Oct 21, 2014

### TheRedDevil18

I'm not sure what form that is. I tried doing it this way but it gets very messy and I don't think it works out

4. Oct 21, 2014

### GFauxPas

The polar, or exponential, form of a complex number is z = |z| ei arg z, did you learn that?

Also, 2 = eln2

Last edited: Oct 21, 2014
5. Oct 21, 2014

### Ray Vickson

Nevertheless, show us what you obtained, messy or not. Anyway, the answer should be messy.

6. Oct 22, 2014

### TheRedDevil18

I tried it and I got up to this stage

(|z| ei arg z)i
= zi e-arg z
= eI lnz e-arg z

And, I'm stuck

7. Oct 22, 2014

### ehild

You can do something with the other side, too. Write it in exponential form.

ehild