Complex Numbers questions
967 published questions with worked solutions.
- Let z be a complex number such that the real part of z - 2i z + 2i is zero. Then, the maximum value of |z − (6 + 8i)| is equal to...
- The sum of the square of the modulus of the elements in the set z = a + ib; a, b ∈ ℤ, z ∈ ℂ, |z − 1| ≤ 1, |z − 5| ≤ |z − 5i| is...
- Let the complex number α and 1 lie on the circles |z – z₀|² = 4 and |z – z₀|² = 16 respectively, where z₀ = 1 + i. Then, the...
- If S = z ∈ C : |z – i| = |z + i| = |z – 1| , then n(S) is:
- If α satisfies the equation x² + x + 1 = 0 and (1 + α)⁷ = A + Bα + Cα², A, B, C ≥ 0 then 5(3A – 2B – C) is equal to ______.
- Let r and θ respectively be the modulus and amplitude of the complex number z = 2 - i (2 5 8 ), then (r, θ) is equal to
- Let α, β be the roots of the equation x² – √6x + 3 = 0 such that Im(α) > Im(β). Let a, b be integers not divisible by 3 and n be...
- If z = 1/2 – 2i is such that |z + 1| = αz + β(1 + i), i = √−1 and α, β ∈ ℝ, then α + β is equal to-
- If z is a complex number, then the number of common roots of the equations z¹⁹⁸⁵ + z¹⁰⁰ + 1 = 0 and z³ + 2z² + 2z + 1 = 0, is...
- If z = x + iy, xy ≠ 0, satisfies the equation z² + i z̄ = 0, then |z²| is equal to :
- Let z₁ and z₂ be two complex numbers such that z₁ + z₂ = 5 and z₁³ + z₂³ = 20 + 15i. Then |z₁⁴ + z₂⁴| equals
- If α denotes the number of solutions of |1 − i|ˣ = 2ˣ and = ( |z| (z) ), where z = 4(1 + i)^4 [ 1 - i + i + - i 1 + i ], i = √−1,...
- If for the complex numbers z satisfying |z-2-2i| 1, the maximum value of |3iz+6| is attained at a + ib, then a + b is equal to...
- The least value of |z| where z is complex number which satisfies the inequality ( (|z|+3)(|z|-1) |z|+1| _e2 ) _ 2 |5 7+9i|, i= -1...
- Let a complex number z, |z| 1, satisfy _ 1 2 ( |z|+11 (|z|-1)^2 ) 2 Then, the largest value of |z| is equal to _____ .
- Let z and w be two complex numbers such that w=z z -2z+2, | z+i z-3i |=1 and Re(w) has minimum value. Then, the minimum value of...
- For |z-1| 2, z lies on and inside the circle of radius 2 units and centre (1, 0). Let S_1, S_2, S_3 be sets defined using this...
- Let a complex number be w = 1- 3i. Let another complex number z be such that |zw| = 1 and arg(z) – arg(w) = 2 . Then the area of...
- Let z_1, z_2 be the roots of the equation z^2+az+12=0 and z_1,z_2 form an equilateral triangle with origin. Then, the value of...
- If z and are two complex numbers such that |z | = 1 and arg(z) – arg( ) = 3 2 , then ( 1-2 z 1+3 z ) is : (Here arg(z) denotes...
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