Problem statement is to find all roots of cos(z) - isin(z) = 0

I know that e^(-iz) = cos(z) - isin(z)

If I were to express e^(-iz) = e^y*e^(-ix) = 0

(since z = x + iy)

either e^y = 0 or e^(-ix) = 0 or both.

e^(-ix) = cos(x) - isin(x). This is never 0.

e^y as a real function of y is also never 0.

Thus, how do I go about finding the roots to this equation?