TS EAMCET Complex Numbers — practice questions
92 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAMCET 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):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) areThe imaginary unit i satisfies i squared equal to which value?What is the value of i to the fourth power?Simplify i raised to the power 102.What is the complex conjugate of 5 - 7i?Add (2 + 3i) and (4 - 5i).Multiply (2 + 3i) by (1 + 2i).What is (1 + i) squared?The reciprocal 1/i simplifies to which complex number?What is the argument of the purely imaginary number i?Find the modulus of the product (3 + 4i)(5 - 12i).For z = 2 + 3i, what is the product of z with its conjugate?In the polar form z = r(cos φ + i sin φ), what does r represent?Two numbers have arguments π/6 and π/3. What is the argument of their product?If |z1| = 2 and |z2| = 3, what is |z1/z2|?Evaluate (cos 30° + i sin 30°)^3 using de Moivre's formula.How many distinct cube roots does a nonzero complex number have?What is the sum of the three cube roots of unity?Which number satisfies z^4 = 1 but does not satisfy z^2 = 1?Which pair gives all the solutions of x^2 + 9 = 0?Every non-constant polynomial with complex coefficients has at least one root in which set?Which two mathematicians are credited with the fundamental theorem of algebra?A real number a is viewed as a complex number. What is its imaginary part?Adding two complex numbers on the complex plane builds which shape from the origin and the points?What is the argument of 5 + 5i in degrees?Hero of Alexandria met a square root of a negative number in which century AD?Solving which equations pushed Italian mathematicians toward complex numbers in the 16th century?Who first described a complex number as a point in a plane in 1799?Who independently published a pamphlet on complex numbers in 1806?Euler's formula expresses e raised to iθ as which expression?By Euler's identity, what is e raised to iπ?A sequence of complex numbers converges exactly when which parts converge?If a + bi is written as a 2 x 2 matrix, the determinant equals which quantity?The study of functions of a complex variable is known by what name?How was taking the square root of a negative number historically regarded?Any non-trivial finite extension field of the reals is isomorphic to which field?In electronics, a phasor with amplitude r and phase φ is written in angle notation. What does r give?If z = 2 - 3i, what is the real part of z squared?Find the modulus of (1 + i) raised to the eighth power.Evaluate (1 + i) raised to the fourth power.Which of these is a square root of -16 in the complex numbers?What are the roots of x^2 - 2x + 5 = 0?A real-coefficient polynomial has 2 + 3i as a root. Which must also be a root?What is the multiplicative inverse of the imaginary unit i?How many distinct fifth roots does the number 1 have in the complex numbers?The argument of z is measured anticlockwise from which axis?