Question

求教一道数学题!P练61急死!已知复数Z满足IZI=1那么I X-1+i I=多少?请解答者不要只给一个答案请写下你宝贵

Answer 1

IZI=1 z=cosx+isinx

Z-1+i =cosx-1+i(sinx+1)

I Z-1+i I=(cosx-1)^2+(sinx+1)^2=1-2cosx+1+2sinx+1=3+2(sinx-cosx)=3+2根号2sin(x-派/4)