Question

Solve \[\sin(x+iy)=0\]

Answer 1

I got \[y=0, x=2\pi n\]Correct?

Answer 2

seems correct.

Answer 3

But are these the only solutions?

Answer 4

they are already infinite....and u know y must be 0 cos sin of imaginary number can't be real

Answer 5

\[\sin(x+iy)=\sin x \cosh y+i \cos x \sinh y\]

Answer 6

*because sin of...

Answer 7

Cosine can- cosh is a real function. It's imaginary for reals, however

Answer 8

cosine can never be imaginary
hyperbolic cos can be...i think this is your point...

Answer 9

Yes. Thanks, I've got it now.