Q 11 :    

Let A={zC : |z 2i|=3}B={zC : Re(z iz)=2} and S=AB. Then zS|z|2 is equal to __________.          [2025]



22

Let z = x + iy.

We have, A : |z – 2 – i| = 3

 |(x2y)+i(y1)|=3  (x2)2+(y1)2=9          ... (i)

Also, B : Re(ziz) = 2

Re((x+y)+i(yx)=2  x+y=2          ... (ii)

From (i) and (ii), we get x=3±172, y=1172

  zS|z|2=14[2×26+2×18]=22.