 Therefore "z" is pure imaginary and cos("y") + "i" sin("y") = 1.Since "y" is real, that happens only if cos("y") = 1 and sin("y") = 0, so that "y" is an integer multiple of 2.Consequently the singular points of this function occur at

The singularities nearest 0, which is the center of the power series expansion, are at ±2"i".