A) 228
B) 144
C) 121
D) 169
Correct Answer: D
Solution :
\[z+|z|=8+12i\] \[\Rightarrow \,\,\,\,x+iy+\sqrt{{{x}^{2}}+{{y}^{2}}}=8+12i\] \[\Rightarrow \,\,\,\,x+\sqrt{{{x}^{2}}+{{y}^{2}}}=8\] ...(i) & \[y=12\] ...(ii) \[(x=-5)\] So, \[z=-5+12i\] \[\Rightarrow \,\,\,\,|z|=\sqrt{25+144}=13\] \[\Rightarrow \,\,\,|{{z}^{2}}|=|z{{|}^{2}}=169\]
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