Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions

Locate the points for which 3 < |z| < 4.

Find the value of 2x⁴ + 5x³ + 7x² – x + 41, when x = `-2 - sqrt(3)"i"`.

Find the value of k if for the complex numbers z₁ and z₂, `|1 - barz_1z_2|^2 - |z_1 - z_2|^2 = k(1 - |z_1|^2)(1 - |"z"_2|^2)`

The real value of ‘a’ for which 3i³ – 2ai² + (1 – a)i + 5 is real is ______.

The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.

If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n²) = ______.

State true or false for the following:

Multiplication of a non-zero complex number by i rotates it through a right angle in the anti-clockwise direction.

State true or false for the following:

The complex number cosθ + isinθ can be zero for some θ.

State true or false for the following:

The argument of the complex number z = `(1 + i sqrt(3))(1 + i)(cos theta + i sin theta)` is `(7pi)/12 + theta`.

State true or false for the following:

The points representing the complex number z for which |z + 1| < |z − 1| lies in the interior of a circle.

State true or false for the following:

If three complex numbers z₁, z₂ and z₃ are in A.P., then they lie on a circle in the complex plane.

State true or false for the following:

If n is a positive integer, then the value of iⁿ + (i)ⁿ⁺¹ + (i)ⁿ⁺² + (i)ⁿ⁺³ is 0.

What is the value of `(i^(4n + 1) -i^(4n - 1))/2`?

What is the smallest positive integer n, for which (1 + i)²ⁿ = (1 – i)²ⁿ?

What is the reciprocal of `3 + sqrt(7)i`.

What is the principal value of amplitude of 1 – i?

What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?

1 + i² + i⁴ + i⁶ + ... + i²ⁿ is ______.

If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.

The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.