# Homework Help: Complex Hyperbolic Property

1. Feb 16, 2012

### nichkis

1. The problem statement, all variables and given/known data

Show: sinh(z + i2(pi)) = sinh(z) using sinh(z) = (ez - e-z)/2

2. Relevant equations

3. The attempt at a solution

So far I have (ex + i(2∏+y) - e-(x+i(2∏+y))/2.

Need help proceeding from here. My thoughts were to define a z' = x + i(2∏+y) but I don't think that I can then say that it is equal to sinh(z) but rather sinh(z').

2. Feb 16, 2012

### Dick

What is $e^{2 \pi i}$? Then use the laws of exponents.

Last edited: Feb 16, 2012
3. Feb 16, 2012

### nichkis

Using the trigonometric construction I was able to get to the answer. Thanks a bunch.