1) If P is a complex number whose modulus is one , then the equation (1+iz1−iz)4 =P has A) real and equal roots B) real and distinct roots C) two real and two complex roots D) all complex roots Answer: Option DExplanation:We have (1+iz1−iz)4 =P ⇒ (i−zi+z)4=P ⇒ (z−iz+i)4=P ⇒ |z−iz+i|4=|P| ⇒ |z−iz+i|4=1 ⇒ |z−i|4=|z+i|4 ⇒ |z-i|=|z+i| ∴ z lies on perpendicular bisector of i and -i ∴ z lies on y-axis ∴ z has all complex roots