Question

if (cos theta -isin theta)^2= x-iy ,prove x^2+y^2 =1

Answer 1

hy
(cos theta-isin theta)2=x-iy
cos sq theta + i sq sin sq theta -2i sin theta cos theta=x-iy. (i sq =-1)
cos sq theta - sin sq theta -2i sin theta cos theta =x-iy
now comparing real and imagi part we get

cos sq theta - sin sq theta=x
y= 2 sin theta

now x sq +y sq = (cos sq theta - sin sq theta) sq + 4sin sq theta cos sq theta

=cos ttp 4 theta + sin ttp 4 theta - 2sin sq
theta cos sq theta +4 sin sq theta cos sq theta. (ttp=to the power )

= cos ttp4 theta + sin ttp 4 theta + 2 sin sq theta cos sq theta
=(cos sq theta + sin sq theta) sq
=(1)sq
= 1 proved

hope it helps u

Answer 2

Step-by-step explanation:

I hope you find its answer