If √a+ib== x + iy, then possible value of √a−ib is
x - iy
√a+ib=x+iy
Squaring on both sides, we get,
a+ib=x2+(iy)2+2ixy⇒ a+ib=(x2−y)2+2ixy∴ a=(x2−y2)and b = 2xy∴ a−ib=(x2−y2)−2ixy⇒ a−ib=x2+i2y2−2ixy [∵ i2=−1]
Taking square root on both sides, we get :
√a−ib=x−iy