List of top Mathematics Questions on Complex numbers asked in IISER

सम्मिश्र संख्याओं के तल में निम्न समुच्चयों पर विचार कीजिए:
\[ A = \left\{ \cos \left(\frac{2n\pi}{5}\right) + i\sin \left(\frac{2n\pi}{5}\right) : n \in \mathbb{Z} \right\} \] तथा
\[ B = \left\{ \cos \left(\frac{2n}{5}\right) + i\sin \left(\frac{2n}{5}\right) : n \in \mathbb{Z} \right\} \].
निम्न कथनों में से कौन सा कथन सत्य है?

Consider the following sets of points in the complex plane \[ A = \left\{ \cos \left( \frac{2n\pi}{5} \right) + i \sin \left( \frac{2n\pi}{5} \right) : n \in \mathbb{Z} \right\} \text{ and} \] \[ B = \left\{ \cos \left( \frac{2n}{5} \right) + i \sin \left( \frac{2n}{5} \right) : n \in \mathbb{Z} \right\} . \] Which of the following statements is TRUE?

Let $z_1, z_2$, and $z_3$ be complex numbers satisfying the following conditions:
\[ 2 = |2z_1| = |z_2 - 1| = |z_3 + 1| = \left| \frac{1}{z_1} + \frac{1}{z_2 - 1} + \frac{1}{z_3 + 1} \right| \]
What is the value of $|4z_1 + z_2 + z_3|$?

Consider the following subset of the $XY$-plane:
$S = \{(|z - iz|, |z|^2) : z \text{ is a complex number}\}$.
Which one of the following statements is Correct ?