BITSAT Complex Numbers — practice questions
35 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice BITSAT Complex Numbers in the app →Find the modulus of the complex number $z = 3 + 4i$.What is the principal argument of the complex number $z = 1 + i$?If $\omega$ is a non-real cube root of unity, find the value of $1 + \omega + \omega^2$.Using De Moivre's theorem, evaluate $\left(\cos\dfrac{\pi}{6} + i in\dfrac{\pi}{6}\right)^6$.The locus of the point $z$ in the Argand plane satisfying $|z - 2| = |z + 2|$ is:If $z = \cos\theta + i in\theta$, find an expression for $z^n + \dfrac{1}{z^n}$.The imaginary unit i is defined as:For z = 3 + 4i, find |z|:The conjugate of z = a + ib is:i² + i³ equals:In polar form z = r(cos θ + i sin θ), r is called the ___ and θ is the ___:For z = a + ib, Re(z) and Im(z) are:Compute (2 + i)(3 - 2i):Find (1 + i)²:Solve z² + 1 = 0:Modulus of z1 z2 where z1 and z2 are complex:Argument of z1 z2:For z = 1 + i, find arg(z):Find z̄ × z (where z = a + ib):Convert i to polar form:DeMoivre's theorem: (cos θ + i sin θ)ⁿ equals:Compute (1 + i)⁸:Cube roots of unity are 1, ω, ω². Find 1 + ω + ω²:Find n-th roots of unity. For z = 1: how many distinct nth roots in complex plane?Find roots of z² - 4z + 5 = 0:If z and z̄ are roots of a quadratic with real coefficients, then sum z + z̄ equals:Locus of z satisfying |z - 1| = |z - i|:If z = cos(π/7) + i sin(π/7), then z⁷ equals:For complex z, |z + i| = |z - i| describes:|z|² = z × z̄. If |z|² = 4 and Re(z) = 1, then Im(z):Find principal argument of -1 - i:For roots of unity ω^n = 1: which is the SMALLEST n such that 1 + ω + ω² + ... + ω^(n-1) = 0?Solve: z² + z + 1 = 0:If z1, z2, z3 are vertices of an equilateral triangle, then:Find (3 + 4i)/(1 + 2i):