[(-根号3+i)/(根号2)]^6=a+bi,其中a与b都是实数,则a=?_数学解答

[(-根号3+i)/(根号2)]^6=a+bi,其中a与b都是实数,则a=?

人气：420 ℃　时间：2020-07-04 12:23:45

解答

a+bi=2^6(-√3/2+0.5i)^6/8
=8(-√3/2+0.5i)^6
=8[COS(5π/6)+iSIN(5π/6)]^6
=8[COS(5π)+iSIN(5π)]
=8(-1+i0)=-8+i0
a=-8