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## Homework Statement

Now, I know there's two ways to go about this and it seems everywhere I look around on the web people are solving it in a way I think that seems longer, harder and more prone to mistakes in exams. It involves using the exponential identities and taking logs. I was shown another way, but unfortunately I haven't quite got the grasp of it.

sinh z = 0

sinh (x + iy) = sinh(x)cos(y) + i cosh(x)sin(y) = 0

So

1) sinh(x)cos(y) = 0

2) cosh(x)sin(y) = 0

(1) Either x = 0 or y = ± Pi/2

(2) cosh (x) is never 0, so therefore x is not 0. Hence y = 0

This is where I'm stuck, I do not know how to go from here.

The answer is z = i*k*Pi