Question

Consider, $f(z)=z^{12}+2\cdot z^{11}+3\cdot z^{10}+\dots ..+12\cdot z+13$ and $\alpha =\cos \frac{2\pi }{13}+i\sin \frac{2\pi }{13}$, where $i=\sqrt{-1}$.
If $S=\left\{z\mid \mathrm{Re}\left(f(z)-z\left(\frac{z^{13}-1}{(z-1{)}^2}\right)\right)=\frac{13}{4}\right\}$, then maximum area of the quadrilateral formed by joining four points lying in $S$ is
[Note: $\mathrm{Re}(z)$ denote the real part of complex number of $z$.

• A. 2
• B. 4
• C. 8
• D. 16

Answer 1

Answer: (C)

Correct answer is (c) 8