## henpen 2 years ago $sin(x+iy)=sin(x)cos(iy)+sin(iy)cos(x)=sin(x)cosh(y)+isinh(y)cos(x)$ $|sin(x+iy)|^2=?$ $|sin(x+iy)|=\sqrt{sin^2xcosh^2y+sinh^2ycos^2x}$ $|sin(x+iy)|^2=sin^2xcosh^2y+sinh^2ycos^2x$

1. henpen

How to get this to equal $sin^2x+sinh^2y$?

2. henpen

$\sin^2x(1-\cosh^2y)=\sinh^2y(\cos^2x-1)$

3. henpen

$\cos^2x-1=-\sin^2x$ $1-\cosh^2y=-\sinh^2y$ Yay!

4. hartnn

haha...u got it almost the same moment i got it..