Find all solutions of the equation, please help, complex analysis?

cos z = 2 i

where z is a complex number, find z?

and i is (iota)

Re: Find all solutions of the equation, please help, complex analysis?

Hint :

Re: Find all solutions of the equation, please help, complex analysis?

I assume you mean that i is the imaginary unit . Anyway

From the first equation, we have or which does not have any real solutions. Substituting x we find

So there you have it, the solutions are .

Re: Find all solutions of the equation, please help, complex analysis?

the answer is (2n + 1)(pi/2) - i ( (-1)^n ) 1.443

where as I got (2n+1)(pi/2) + 1.443