# Log of Complex Variable

1. Jun 16, 2012

### baby_1

what is log of z=X+JY?

Thanks

2. Jun 16, 2012

### Infinitum

Did you try to find out what it would be??

Here.

3. Jun 16, 2012

### HallsofIvy

Staff Emeritus
We can always write x+ iy in "polar form": $x+ iy= re^{i\theta}$ where $r= \sqrt{x^2+ y^2}$ and $\theta= arctan(y/x)$.

Then $ln(x+ iy)= ln(re^{i\theta})= ln(r)+ i\theta$. Of course, because tangent is periodic, with period $\pi$, ln is not a single-valued function:
$ln(x+ iy)= ln(r)+ i(\theta+ n\pi)$ for n any integer.

4. Jun 16, 2012

### baby_1

Thanks

5. Jun 16, 2012

### pashav46

ln(x+iy)=ln(r)+i(θ+2*nπ) for n any integer.