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1)

If P is a complex number whose modulus is one , then the equation (1+iz1iz)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 D

Explanation:

We have

 (1+iz1iz)4  =P

      (izi+z)4=P

    (ziz+i)4=P

      |ziz+i|4=|P|

   |ziz+i|4=1

     |zi|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