Your answer is (half) correct, because . See here, for example. You can get the other half of the answer by following through what happens if you use instead of
The question
Find all solutions to of:
cosh(z) = 2i
My attempt
//multiply by
//complete the square
so
//since exp is periodic
Since z = x + iy,
However, the solution is actually:
I'm confused, my working looks correct. :/ Any help would be greatly appreciated!
You should know that .
So you are solving .
Equating real and imaginary parts gives and .
Solving the first equation: Since for all , that means , where .
Substituting into the second equation gives
So the solution is , where .