What is the Log of a Complex Variable?

[baby_1]

what is log of z=X+JY?

Thanks

 

[Infinitum]

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

Here.

 

[HallsofIvy]

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.

 

[baby_1]

Thanks

 

[pashav46]

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