Complex number

Question

Evaluate in Cartesian form: arc tan(2i)

Answer 1

arctan(2i) = i arctanh(2)
But that's not much help, since arctanh(x) has a domain os |x| < 1
So, fall back on the definition: arctanh(x) = 1/2 ln (1+x)/(1-x)
So now you have
arctan(2i) = i/2 ln ((1+2i)/(1-2i)) = i/2 ln(-3/5 + 4/5 i)

Now just evaluate complex logs in the normal ways.