Algebra Complex Numbers Mock Tests

Let z be a complex number such that |z| = 1 and arg(z) in [0, 2pi). The number of distinct values of z satisfying z^6 + z^3 + 1 = 0 is

Let z be a complex number satisfying |z - 1| = 1 and Re(z²) = 0. The number of such complex numbers z is

Let ω be a complex cube root of unity with ω ≠ 1. If (2 + ω)(2 + ω²) = 3^k, then k equals:

The locus of a complex number z satisfying |z - 1| = |z + 1| is:

If z is a complex number such that |z| = 1 and z = e^(iθ) with 0 < θ < pi, then the argument of (z - 1)/(z + 1) is equal to:

Let z be a complex number such that |z − 1| = 1 and z ≠ 0. If z^6 = z̅^6, then the smallest positive integer n such that z^n is real for all such z is:

Let S = {z ∈ ℂ : |z - 2| ≤ 2 and |Re(z)| ≤ 1}. If z₀ is a point in S such that |z₀| is maximum, then the number of elements in the set {z ∈ S : |z - z₀| = |z₀|} is equal to:

The number of distinct complex numbers z satisfying z¹² = 1 and Re(z) > 0 is: