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QJEEM24Mae563: JEE Main 2024 Mathematics - Class 11 JEEM24Mae563 Solution: The sum of the square of the modulus of the elements in the set …

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,∣z−5∣≤∣z−5i∣}\{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 __________.

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JEE Main 2024 (Online) 9th April Morning Shift Mathematics - Complex Numbers Question 19 English Explanation

zz should be lying in the shaded region shown in adjacent figure.

Possible zz are

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

Sum of squares of modulus

amp;=0+1+4+2+2amp;=9\begin{aligned}& =0+1+4+2+2 \\& =9\end{aligned}

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