Complex Numbers questions
967 published questions with worked solutions.
- If x^2 + x + 1 = 0, then the value of (x + 1 x )^4 + (x^2 + 1 x^2 )^4 + (x^3 + 1 x^3 )^4 + + (x^ 25 + 1 x^ 25 )^4 is :
- Let = -1+i 3 2 and = -1-i 3 2 , i = -1 . If (7-7 +9 )^ 20 +(9+7 -7 )^ 20 +(-7+9 +7 )^ 20 +(14+7 +7 )^ 20 = m^ 10 , then m is...
- Let S = z C : 4z^2 + z = 0 . Then _ z S |z|^2 is equal to :
- Let S = z: 3 |2z-3(1+i)| 7 be a set of complex numbers. Then Min _ z S |z+ 1 2 (5+3i) | is equal to :
- If z = 3 2 + i 2 , i = -1 , then (z^ 201 - i)^8 is equal to
- Let S = z C : | z-6i z-2i | = 1 and | z-8+2i z+2i | = 3 5 . Then _ z S |z|^2 is equal to
- Let z=(1+i)(1+2i)(1+3i) (1+ni), where i= -1 . If |z|^2=44200, then n is equal to -
- Let z be a complex number such that |z-6| = 5 and |z+2-6i| = 5. Then the value of z^3 + 3z^2 - 15z + 141 is equal to
- Let A= z C: |z-2| 4 and B= z C: |z-2|+|z+2|=5 . Then the max |z_1-z_2|: z_1 A and z_2 B is
- Let z1, z2 and z3 be three complex numbers on the circle |z| = 1 with arg (z1) = - 4 , arg(z2) = 0 and arg(z3) = 4 . If |z_1 z_2...
- The number of complex numbers z, satisfying |z| = 1 and | z z + z z | = 1, is
- Let | z -i 2 z +i | = 1 3 , Z ∈ C, be the equation of a circle with center at C. If the area of the triangle, whose vertices are...
- If and are the roots of the equation 2z^2 - 3z - 2i = 0, where i = -1 , then 16. Re ( ^ 19 + ^ 19 + ^ 11 + ^ 11 ^ 15 + ^ 15 ). Im...
- Let O be the origin, the point A be z_1 = 3 + 2 2 i, the point B(z_2) be such that 3 |z_2| = |z_1| and arg (z_2) = (z_1) + 6 ....
- Let integers a, b [–3, 3] be such that a + b 0. Then the number of all possible ordered pairs (a, b), for which | z-a z+b |=1 and...
- If z_1, z_2, z_3 C are the vertices of an equilateral triangle, whose centroid is z_0, then _ k=1 ^ 3 (z_k - z_0)^2 is equal to
- Let A = z ∈ ℂ : |z − 2 − i| = 3 , B = z ∈ ℂ : Re(z − iz) = 2 and S = A∩B. Then _ z S |z|^2 is equal to _____.
- Let be a solution of x^2 + x + 1 = 0, and for some a and b in R, [4 a b] bmatrix 1 & 16 & 13 -1 & -1 & 2 -2 & -14 & -8 bmatrix =...
- Let the product of _1 = (8 + i) + (7 + 4i) and _2 = (1 + 8i) + (4 + 7i) be + i , i = -1 . Let p and q be the maximum and the...
- If is a root of the equation x^2 + x + 1 = 0 and _ k=1 ^ n ( ^k + 1 ^k )^2 = 20, then n is equal to _____.
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