JEE MAIN - Mathematics (2024 - 9th April Morning Shift - No. 27)
The sum of the square of the modulus of the elements in the set $$\{z=\mathrm{a}+\mathrm{ib}: \mathrm{a}, \mathrm{b} \in \mathbf{Z}, z \in \mathbf{C},|z-1| \leq 1,|z-5| \leq|z-5 \mathrm{i}|\}$$ is __________.
Answer
9
Explanation
_9th_April_Morning_Shift_en_27_1.png)
$$z$$ should be lying in the shaded region shown in adjacent figure.
Possible $$z$$ are
$$z=0+0 i,(1+0 i),(2+0 i),(1-i),(1+i)$$
Sum of squares of modulus
$$\begin{aligned} & =0+1+4+2+2 \\ & =9 \end{aligned}$$
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