TS EAPCET (Engineering) De Moivre's Formula — practice questions
32 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAPCET (Engineering) De Moivre's Formula in the app →For any integer n, (cos θ + i sin θ)ⁿ is equal to which expression?(cos θ + i sin θ)³ equals which of the following?Evaluate (cos 60° + i sin 60°)³.What is (cos 45° + i sin 45°)⁸ equal to?Simplify (cos 45° + i sin 45°)⁴.By Euler's form e^(iθ) = cos θ + i sin θ, the power (e^(iθ))ⁿ equalsWhat is the modulus of (cos θ + i sin θ)⁷ for real θ?The argument of (cos θ + i sin θ)⁵ isDe Moivre's theorem is first proved for natural numbers usingHow many distinct values does the expression z^(1/4) have for a nonzero z?A nonzero complex number has how many distinct cube roots?If ω is a complex cube root of unity, what is the value of ω³?The non-real cube roots of unity areWhich set contains all the fourth roots of unity?The sixth roots of unity are the vertices of a regular polygon with how many sides?All nth roots of unity lie on a circle in the complex plane of radiusHow many of the seventh roots of unity are primitive?The equation z⁸ = 1 has how many complex roots?The reciprocal of an nth root of unity isUnder multiplication, the roots of unity form which kind of structure?Evaluate (√3 + i)⁶.Comparing real parts in (cos θ + i sin θ)² gives cos 2θ equal toWhich identity for sin 3θ follows from expanding (cos θ + i sin θ)³?The expression for cos nx in terms of cos x gives which family of polynomials?The three cube roots of 8 in the complex plane areThe principal fourth root of -1 has argumentAdjacent sixth roots of unity differ in argument byBy Euler's formula, e^(iπ) equalsDe Moivre's formula can be derived from the exponential law together with which result?If a complex number z has modulus 2, the modulus of z⁵ isFor a cube root of unity ω, the value of 1 + ω² + ω⁴ isIf ω is a non-real cube root of unity, (1 + ω)³ equals