- #1

bonfire09

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## Homework Statement

I have to find ##\tan^{-1}(2i)##.

## Homework Equations

## The Attempt at a Solution

So far I have ##\tan^{-1}(2i)=z\iff tan z= 2i\iff \dfrac{sin z}{cos z}=2i ##. From here I get that

##-3=e^{-2zi}##. I do no know how to take it further to get ##z=i\dfrac{\ln 3}{2}+(\dfrac{\pi}{2}+\pi n)##. Should I use natural logarithms but the problem is that I have a ##-3## which won't allow me to take the natural log of both sides. Any help would be great thanks.