- #1
Carl140
- 49
- 0
Homework Statement
Let z be a complex number. I want to solve cos(z)= -i*sin(z).
The Attempt at a Solution
Here's my work:
cos(z) = -i*sin(z) implies cos(z) + isin(z) = 0.
Therefore exp(i*z) = 0. Now put z= x+iy then i*z = i*(x+iy) = ix - y, hence
exp(i*z) = exp(ix-y) = exp(ix)*exp(y) =0 but exp(y) is always nonzero so this implies
exp(i*x) = 0 hence cos(x)+i*sin(x) =0 thus cos(x)=0 and sin(x)=0 which is impossible.
So I think there are no solutions. Is this correct?