List of top Mathematics Questions on Complex Numbers asked in IPU CET

What is the value of $i^{99}$ (where $i$ is the imaginary unit)?
If $n$ is an integer, compute the value of the fraction \[ \frac{(1 + \theta)^n}{(1 - \theta)^{n-2}} \]

Choose the most appropriate options. 
If \( |z^2 - 1| = |z|^2 + 1 \), then \( z \) lies on a

$ (1 + 2i)^6 $ is equal to:

What is the number of ordered pairs of real numbers (a, b) such that \[ (a + bi)^{2002} = a - bi \]
Let \( a = \cos \theta_1 + i \sin \theta_1 \), \( b = \cos \theta_2 + i \sin \theta_2 \), \( c = \cos \theta_3 + i \sin \theta_3 \) and \( a + b + c = 0 \), then \[ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = ? \]
Which of the following complex numbers is conjugate to its square?