题目

复数（-1+√3i）^5/1+√3i的值

提问时间：2020-10-28

答案

（-1+√3i）^5/1+√3i
(-1+√3i)^5 = 2^5 * (-1/2 + i√3/2)^5 = 2^5 * (cos(2π/3) +isin(2π/3))^5
= 2^5 * (e^(i2π/3))^5 = 32 * e^(i10π/3)
1+√3i = 2 * (1/2 + i√3/2)^5 =2 * (cos(π/3) +isin(π/3))= 2 * e^(iπ/3)
(-1+√3i)^5 / (1+√3i ) ＝ 32 * e^(i10π/3) / (2 * e^(iπ/3)) = 16 * e^(i9π/3)
= 16 e^(i3π) = 16 e^(iπ) = 16 (cos(π) +isin(π))= -16 答案：负16