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

What is the polar form of the complex number (i²⁵)³?

The amplitude of `sin  pi/5 + i(1 - cos  pi/5)` is ______.

Show that the complex number z, satisfying the condition arg`((z - 1)/(z + 1)) = pi/4` lies on a circle.

If arg(z – 1) = arg(z + 3i), then find x – 1 : y. where z = x + iy.

z₁ and z₂ are two complex numbers such that |z₁| = |z₂| and arg(z₁) + arg(z₂) = π, then show that z₁ = `-barz_2`.

If for complex numbers z₁ and z₂, arg (z₁) – arg (z₂) = 0, then show that `|z_1 - z_2| = |z_1| - |z_2|`.

Write the complex number z = `(1 - i)/(cos  pi/3 + i sin  pi/3)` in polar form.

If z and w are two complex numbers such that |zw| = 1 and arg(z) – arg(w) = `pi/2`, then show that `barz`w = –i.

arg(z) + arg`barz  (barz ≠ 0)` is ______.

If |z| = 4 and arg(z) = `(5pi)/6`, then z = ______.

State True or False for the following:

Let z₁ and z₂ be two complex numbers such that |z₁ + z₂| = |z₁| + |z₂|, then arg(z₁ – z₂) = 0.

Find z if |z| = 4 and arg(z) = `(5pi)/6`.

Find principal argument of `(1 + i sqrt(3))^2`.

|z₁ + z₂| = |z₁| + |z₂| is possible if ______.

The value of arg (x) when x < 0 is ______.

Find the linear inequalities for which the shaded region in the given figure is the solution set.

Solve the following system of inequalities `(2x + 1)/(7x - 1) > 5, (x + 7)/(x - 8) > 2`

Find the linear inequalities for which the shaded region in the given figure is the solution set.

Show that the following system of linear inequalities has no solution x + 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1

Solve the following system of linear inequalities:

3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4