# Complex numbers basics

1. May 13, 2016

### Dousin12

1. Give a formula for the values on m such that z^m=z

z=cos(7pi/6)+i*sin(7pi/6)

2. If i use de movires i get

3. m*7pi/6=7pi/6 + k*2pi

But then i get the value that k=12/7, Which is the wrong formula.

The correct answer is 1+12k for k=0,1,2...

2. May 13, 2016

### SammyS

Staff Emeritus

Can you show us your work ?

3. May 13, 2016

### Dousin12

m*7pi=7pi+k*12pi
m=1+12k/7

Okay, i got closer to the right answer now

Which is the equation wolfram alpha also get if i post my original equation. So it must be something wrong!!!

1+12k is the correct!!

4. May 13, 2016

### SammyS

Staff Emeritus
You have $\ m=1+\frac{12}{7}k\,,\$ & k must be some integer. I suppose from the context of the question that m must also be an integer.

m will only be an integer if k is an integer multiple of 7 , Right ?

let k = 7n .