求教,复数幂指数的运算法则.如：Z1=3exp（iθ1）,Z2=4exp（iθ2）,那么Z1/Z2=?

设z1=ae^(iθ1)=a(cos(θ1)+isin(θ1))
z2=be^(iθ2)=b(cos(θ2)+isin(θ2))
z1/z2=(a/b)[(cos(θ1)+isin(θ1))]/[(cos(θ2)+isin(θ2))]
[(cos(θ1)+isin(θ1))]/[(cos(θ2)+isin(θ2))]
=[(cos(θ1)+isin(θ1))][(cos(θ2)-isin(θ2))]/[(cos(θ2))^2+(sin(θ2))^2]
=[(cos(θ1)cos(θ2)+sin(θ1)sin(θ2))+i(sin(θ1)cos(θ2)-cos(θ1)sin(θ2))/1
=cos(θ1-θ2)+isin(θ1-θ2)
=e^(i(θ1-θ2))
所以z1/z2=a/b*e^(i(θ1-θ2))
例如Z1=3e^（iθ1）,Z2=4^（iθ2）
Z1/Z2=3/4*e^(i(θ1-θ2))