List of top Mathematics Questions on Complex numbers asked in BITSAT

If \( z = x + iy \) is a complex number such that \( |z - 1| = |z + 1| \), then the locus of \( z \) represents:

If \( z = 2(\cos 60^\circ + i \sin 60^\circ) \), find the value of \( z^3 \).

If \( |z_1| = 2, |z_2| = 3, |z_3| = 4 \) and \( |2z_1 + 3z_2 + 4z_3| = 4 \), then the absolute value of \( 8z_2z_3 + 27z_1z_3 + 64z_1z_2 \) equals:

If \( z_1, z_2, \dots, z_n \) are complex numbers such that \( |z_1| = |z_2| = \dots = |z_n| = 1 \), then \( |z_1 + z_2 + \dots + z_n| \) is equal to:

If \( z, \bar{z}, -z, -\bar{z} \) forms a rectangle of area \( 2\sqrt{3} \) square units, then one such \( z \) is:

If f(z)=dfrac7-z1-z², where z=1+2i, then |f(z)| is equal to

If z₁=\sqrt3+i\sqrt3 and z₂=\sqrt3+i, then the complex number ((z₁)/(z₂))⁵0 lies in the

If the amplitude of \(z - 2 - 3i\) is \(\pi/4\), then the locus of \(z = x + i y\) is:

If \(f(z) = \frac{7 - z}{1 - z^2}\), where \(z = 1 + 2i\), then \(|f(z)|\) is equal to

If complex numbers \(z_1,z_2\) and \(0\) are vertices of an equilateral triangle, then \(z_1^2+z_2^2-z_1z_2\) is equal to

If the real part of \( \frac{z + 1}{z - 1} = 4 \), then the locus of the point representing \( z \) in the complex plane is

The amplitude of \( \sin \frac{\pi}{5} + i \left( 1 - \cos \frac{\pi}{5} \right) \) is:

If 1-iα1+iα=A+iB, then A²+B² equals