List of top Mathematics Questions on Complex numbers asked in JEE Main

The equation \(\arg\left(\frac{z - 1}{z + 1}\right) = \frac{\pi}{4}\) represents a circle with :

Let \( z = \frac{1 - i\sqrt{3}}{2}, \, i = \sqrt{-1} \). Then the value of

\[ 21 + \left( z + \frac{1}{z} \right)^3 + \left( z^2 + \frac{1}{z^2} \right)^3 + \left( z^3 + \frac{1}{z^3} \right)^3 + \dots + \left( z^{21} + \frac{1}{z^{21}} \right)^3 \] is _________.

The least positive integer n for which $\left( \frac{1 + i \sqrt{3}}{1 - i \sqrt{3}} \right)^n = 1 $, is :

The least positive integer n such that $1-\frac{2}{3}-\frac{2}{3^{2}}-.......-\frac{2}{3^{n-1}} < \frac{1}{100},$ is :

If (z)²+|z|=0 and if α is sum of roots and β is product of non-zero roots, then find 4(α²+β²)

Find the range of \(\frac{1}{7}-\sin5x\)

If the complex number (1 + 2i cosθ) / (1 - 3i cosθ) is purely imaginary, then find the number of values of θ in the interval [-2π, 2π].

If set A = { z: |z - 1| ≤ 1} and set B = { z: |z - 5i| ≤ |z - 5| }, if z = a + ib, where a, b ∈ I, then find the sum of modulus squares of A ∩ B.