The sum of the square of the modulus of the elements in the set z=a+ib:a,b Z,z C,|z-1| 1,|…

Question

The sum of the square of the modulus of the elements in the set ${z=a+ib:a,b\in Z,z\in C,|z-1|\le 1,|z-5|\le |z-5i|}$ is \_\_\_\_\_\_\_\_\_\_.

Answer: 9

Accepted Answer

$z$ should be lying in the shaded region shown in adjacent figure.

Possible $z$ are

$z=0+0i,(1+0i),(2+0i),(1-i),(1+i)$

Sum of squares of modulus

$\begin{gathered} =0+1+4+2+2 \ =9 \end{gathered}$

Solutions · 1