TS EAMCET Complex Numbers and Quadratic Equations — practice questions
94 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAMCET Complex Numbers and Quadratic Equations 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):The value of i⁴ⁿ⁺³ (n a positive integer) isThe modulus of the complex number 3 + 4i isThe conjugate of (2 − 3i) isIf z = 1 + i, then z² equalsThe argument (principal value) of the complex number i isThe multiplicative inverse of (3 + 4i) isFor complex numbers, which relation is NOT defined?The roots of x² + 1 = 0 areIf z = a + ib is purely imaginary, thenThe value of (1 + i)/(1 − i) is|z₁ z₂| equalsIn z = a + ib, Re(z) and Im(z) areWhat is the value of i squared, where i is the imaginary unit?Simplify i cubed.What does i to the power 4 equal?For any integer k, what is i raised to 4k + 3?What is the value of 1/i, written as a complex number?Evaluate i to the power -2.Find i^10 using the cycle of powers of i.What is i^27 equal to?If 4x + i(3x - y) = 3 - 6i for real x and y, find x.Given 4x + i(3x - y) = 3 + i(-6), with x and y real, what is y?The complex numbers a + ib and c + id are equal exactly whenSubtract 2 - i from 6 + 3i, that is, find (6 + 3i) - (2 - i).Expand and simplify (1 + i) squared.For real a and b, (a + ib)(a - ib) simplifies toSimplify the quotient (1 + i)/(1 - i).Find the modulus of 2 - 5i.For complex z1 and z2, the modulus of their product isThe conjugate of a sum z1 + z2 equalsA complex number is real if and only if itWhat do you get when a complex number is conjugated twice?In the Argand plane, x + iy is represented by which point?The conjugate of z is its reflection across which line?Points on the y-axis of the Argand plane stand for numbers of the formWhich complex number matches the point (-2, 3) in the Argand plane?Find the conjugate of (3 - 2i)(2 + 3i) / ((1 + 2i)(2 - i)).If x + iy = (a + ib)/(a - ib) with a, b real, then x^2 + y^2 equalsWhich two numbers are the square roots of -1?Express the square root of -3 in terms of i.Using i-notation, what is (√-2)(√-3)?Solve x^2 + 1 = 0 over the complex numbers.A quadratic ax^2 + bx + c with D = b^2 - 4ac < 0 has roots that areWith r the modulus and phi the argument, the polar form of z isIn a polar-form product, what happens to moduli and arguments?When dividing z1 by z2 in polar form, the argument of the quotient isDe Moivre's formula gives (cos t + i sin t) to the power n asEvaluate (cos 30 deg + i sin 30 deg) cubed.Evaluate (1 + i)^8.A nonzero complex number has how many distinct n-th roots, n a positive integer?Which set lists all four fourth roots of 1?With w a complex cube root of unity, (1 + w)^2 equalsIf w is a cube root of unity, what is w^10?Which formula did Euler obtain in 1748 for complex analysis?What is e raised to i times pi?Geometrically, the sum of two complex numbers is found using aWhy do electrical engineers write j instead of i?Which of these numbers is purely imaginary?What is the sum i + i^2 + i^3 + i^4?