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?