TS EAMCET Algebra: De Moivre's Theorem — practice questions
53 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAMCET Algebra: De Moivre's Theorem in the app →For real x and integer n, (cos x + i sin x)^n is equal to which expression?In how many ways can cos x + i sin x be abbreviated, and what is the usual short form?The theorem connecting powers of cos x + i sin x to multiple angles is named after which mathematician?Raise cos 30° + i sin 30° to the third power. What number results?Evaluate (cos 60° + i sin 60°)^6.What does (cos θ + i sin θ)^−1 equal?What is the modulus of cos x + i sin x when x is real?Using polar form, find the eighth power of the complex number 1 + i.What is (1 + i)^4 in simplest form?For z = cos θ + i sin θ, z^n added to its reciprocal power gives what?Taking the real part of (cos x + i sin x)^3 yields cos 3x as what?Expanding (cos x + i sin x)^2 and comparing real parts gives cos 2x equal to what?Comparing imaginary parts in the expansion of (cos x + i sin x)^2 gives sin 2x equal to what?Equating real parts of both sides of de Moivre's formula yields an expression for which quantity?How many cube roots of unity exist among the complex numbers?State the cube of any primitive cube root of unity ω.If ω is a non-real cube root of unity, then 1/ω equals which value?For a primitive cube root of unity ω, find (1 + ω − ω^2) cubed.The reciprocal of an n-th root of unity is equal to which related number?What is the modulus of every complex n-th root of unity?Which collection lists every complex solution of z^4 = 1?De Moivre's formula as written is valid for which exponents n?Euler's totient of 12 counts how many primitive 12th roots of unity?Which of these is a cube root of −1 other than −1 itself?Among the fourth roots of −1, what is the smallest positive argument?What is the angle between consecutive points representing the sixth roots of unity?Find the tenth power of (1 + i√3)/(1 − i√3) in rectangular form.If z + 1/z = 1, what is z^100 + 1/z^100?For nonzero complex z, how many distinct values does z^(3/4) take?A non-integer power of a complex number gives what kind of result?Which method of proof is used to establish de Moivre's theorem for natural numbers?De Moivre's formula can be derived from Euler's formula together with which law?De Moivre's formula links complex numbers with which branch of mathematics?The formula for cos nx in powers of cos x is which classical polynomial family?Which number satisfies the equation z^6 = 1?Which is the hyperbolic analogue of de Moivre's formula?The 9th power of cos 20° + i sin 20° is which value?The abbreviation cis x stands for which complex expression?What is (1 + i root 3)^3?(cos 45° + i sin 45°)^2 equals(cos x - i sin x)^n equals which expression for integer n?Which identity lets us derive de Moivre's formula using the exponential law for integer powers?How is the proof of de Moivre's formula for positive integers usually established?A number z is an nth root of unity when it satisfies which equation?The fourth roots of unity in the complex plane areGeometrically, the nth roots of unity lie at the vertices ofConsecutive sixth roots of unity differ in argument byHow many primitive 12th roots of unity are there?If n is a prime number such as 7, how many nth roots of unity are primitive?Under multiplication, the nth roots of unity form which type of group?Using the cube roots of unity 1, w, w^2, the value of 1 + w + w^2 isEach of the four fourth roots of 16 has modulusFor even n, which real numbers are nth roots of unity?