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1)

Let a,b,x and y be real numbers such that a-b=1 and y≠ o. If the complex number z=x+iy satisfies  Im(az+bz+1)=y , then which of the following is(are) possible value(s) of x?


A) 11+y2

B) 11y2

C) 1+1+y2

D) 1+1y2

Answer:

Option B,D

Explanation:

az+bz+1=ax+b+aiy(x+1)+iy

=(ax+b+aiy)((x+1)iy)(x+1)2+y2

   Im(az+b)z+1)=(ax+b)y+ay(x+1)(x+1)2+y2

     (ab)y(x+1)2+y2=y

    a-b=1

   (x+1)2+y2=1

    x=1±1y2