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

If z₁ and z₂ are complex numbers such that z₁ + z₂ is a real number, then z₂ = ______.

If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.

State True or False for the following:

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

State True or False for the following:

For any complex number z the minimum value of |z| + |z – 1| is 1.

State True or False for the following:

The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).

State True or False for the following:

The inequality |z – 4| < |z – 2| represents the region given by x > 3.

Find `|(1 + i) ((2 + i))/((3 + i))|`.

Where does z lie, if `|(z - 5i)/(z + 5i)|` = 1.

The real value of α for which the expression `(1 - i sin alpha)/(1 + 2i sin alpha)` is purely real is ______.

The value of `(z + 3)(barz + 3)` is equivalent to ______.

If `((1 + i)/(1 - i))^x` = 1, then ______.

A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α² + β² = ______.

Which of the following is correct for any two complex numbers z₁ and z₂?

The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.

Let x, y ∈ R, then x + iy is a non-real complex number if ______.

If a + ib = c + id, then ______.

The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.

If z is a complex number, then ______.

In how many ways can 5 children be arranged in a line such that two particular children of them are always together 

In how many ways can 5 children be arranged in a line such that two particular children of them are never together.