z=cosΦ+sinΦi
z·z = (cosΦ+sinΦi) x (cosΦ+sinΦi) = (cosΦ)^2 - (sinΦ)^2 + 2sinΦcosΦi = -1
则有
(cosΦ)^2 - (sinΦ)^2 = 2(cosΦ)^2 -1 = cos2Φ = -1 且2cosΦsinΦ = sin2Φ = 0
那么就有
2Φ = π + 2kπ (k为整数)
可得
Φ = 0.5π + kπ (k为整数)
z=cosΦ+sinΦi
z·z = (cosΦ+sinΦi) x (cosΦ+sinΦi) = (cosΦ)^2 - (sinΦ)^2 + 2sinΦcosΦi = -1
则有
(cosΦ)^2 - (sinΦ)^2 = 2(cosΦ)^2 -1 = cos2Φ = -1 且2cosΦsinΦ = sin2Φ = 0
那么就有
2Φ = π + 2kπ (k为整数)
可得
Φ = 0.5π + kπ (k为整数)