The question:

Find all solutions of sinh(z) = 0

My attempt:

sinh(z) = sinh(x)cos(y) + icosh(x)sin(y)

Equating real and imaginary parts:

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

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

For (1):

sinh(x) = 0 when x = 0, and cos(y) = 0 when

Sub these values into (2):

cosh(0) = 1 (therefore, we need sin(y) = 0)

is never 0.

So it appears that it never equals zero. However, my text states that it does when Where have I gone wrong? Thanks.