Question

复数的三角形式及运算计算（√3/2+(1/2)i)^15怎么算,

Answer 1

计算[√3/2+(1/2)i]¹⁵怎么算,

r=√[(√3/2)²+(1/2)²]=1；tanθ=(1/2)/(√3/2)=1/√3=√3/3,故θ=π/6;

于是原式=[cos(π/6)+isin(π/6)]¹⁵=cos(15π/6)+isin(15π/6)=cos(5π/2)+isin(5π/2)

=coa(2π+π/2)+isin(2π+π/2)=cos(π/2)+isin(π/2)=i