 We solve

by recalling that if "z" = "x" + "iy" and "e" "iy" = cos("y") + "i" sin("y") then

and then take "x" and "y" to be real.Since "y" is real, the absolute value of cos("y") + "i" sin("y") is necessarily 1.Therefore, the absolute value of "e" "z" can be 1 only if "e" "x" is 1; since "x" is real, that happens only if "x" = 0.