AP EAPCET (Engineering) Complex Numbers and Quadratic Equations — practice questions
87 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) 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?The value of i cubed equals which of these?Evaluate i^1001.What is i^2002 equal to?The reciprocal of i, written i^(-1), simplifies toSimplify i^(-3).For the complex number 3 - 7i, what is the imaginary part?Add (2 + 3i) and (-6 + 5i). The result isSubtract (2 - i) from (6 + 3i).The product of (3 + 5i) and (2 + 6i) isIf 4x + i(3x - y) = 3 - 6i with x and y real, then y equalsThe additive identity in the set of complex numbers isWhich complex number serves as the multiplicative identity?The product of a complex number z and its conjugate equalsWhich point of the plane represents the complex number 2 + 4i?Numbers of the form a + i0 lie on which axis of the Argand plane?On the Argand plane, the number 0 + ib lies on theThe plane where every point stands for a complex number is called theThe symbol for the square root of -3 is taken to meanThe square of the number √3 i equalsThe two square roots of -1 areIn standard form, (1 + i)/(1 - i) equalsWrite 1/(1 + i) in the form a + ib.The standard form of (2 + i)/(2 - i) isWhen two complex numbers in polar form are multiplied, their arguments areFor the quotient z1/z2 in polar form, the argument of the result isWhich mathematician in 1730 linked multiple-angle trigonometric identities to powers of complex numbers?In which year did Euler obtain his formula connecting the exponential with sine and cosine?A nonzero complex number has how many distinct n-th roots?Which of these is NOT a fourth root of 1?The solutions of x^2 + 4 = 0 over the complex numbers areIf 1, ω and ω^2 are the cube roots of unity, then 1 + ω + ω^2 equalsFor a cube root of unity ω, the value of ω^3 isThe modulus of a non-real cube root of unity isWhich equation shows that the real number system needs extending?If |z| = 1, then the conjugate of z equalsThe set of points with |z| = 1 in the complex plane formsThe sum of z and its conjugate always equalsThe real part of (2 + i)^2 isEvery real number a can be regarded as the complex number