What is period of function sine hyperbolic sinh(z)?

1 Answer
Jul 5, 2016

The period #2pi# for #z=|z|e^(i arg z)#, in its #arg z# is indeed the period for #f(z)=sinh z#.

Explanation:

Let #z=r e^(itheta)=r(cos theta + i sin theta)=z(r, theta)=|z|e^( i arg z).#.

Now, #z=z(r, theta)=z(r, theta+2pi)#

So, #sinh (z(r, theta+2pi)=sinh (z(r, theta)=sinh z#,

Thus sinh z is periodic with period 2pi in arg z = theta#.