Arts (English Medium) Class 11 - CBSE Question Bank Solutions

The equation |z + 1 – i| = |z – 1 + i| represents a ______.

Number of solutions of the equation z² + |z|² = 0 is ______.

For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"n"`

Evaluate `sum_(n = 1)^13 (i^n + i^(n + 1))`, where n ∈ N.

If `((1 + i)/(1 - i))^3 - ((1 - i)/(1 + i))^3` = x + iy, then find (x, y).

If `(1 + i)^2/(2 - i)` = x + iy, then find the value of x + y.

If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.

If z = x + iy, then show that `z  barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.

If the real part of `(barz + 2)/(barz - 1)` is 4, then show that the locus of the point representing z in the complex plane is a circle.

Solve the equation |z| = z + 1 + 2i.

If |z + 1| = z + 2(1 + i), then find z.

If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.

If |z₁| = 1(z₁ ≠ –1) and z₂ = `(z_1 - 1)/(z_1 + 1)`, then show that the real part of z₂ is zero.

If |z₁| = |z₂| = ... = |z_n| = 1, then show that |z₁ + z₂ + z₃ + ... + z_n| = `|1/z_1 + 1/z_2 + 1/z_3 + ... + 1/z_n|`.

Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.

For any two complex numbers z₁, z₂ and any real numbers a, b, |az₁ – bz₂|² + |bz₁ + az₂|² = ______.

The value of `sqrt(-25) xx sqrt(-9)` is ______.

The number `(1 - i)^3/(1 - i^2)` is equal to ______.

The sum of the series i + i² + i³ + ... upto 1000 terms is ______.

Multiplicative inverse of 1 + i is ______.