NCERT solutions for Class 11 Mathematics chapter 5 - Complex Numbers and Quadratic Equations [Latest edition]

Express the given complex number in the form a + ib: `(5i) (- 3/5 i)`

Express the given complex number in the form a + ib: i^–39

Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`

Express the given complex number in the form a + ib : `[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`

Express the given complex number in the form a + ib: `(1/3 + 3i)^3`

Express the given complex number in the form a + ib: `(-2 - 1/3 i)^3`

Find the multiplicative inverse of the complex number –i

Express the following expression in the form of a + ib.

`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`

Find the modulus and the argument of the complex number  `z = – 1 – isqrt3`

Find the modulus and the argument of the complex number `z =- sqrt3 + i`

Convert the given complex number in polar form `sqrt3 + i`

Solve the equation x² + 3 = 0

Solve the equation 2x² + x + 1 = 0

Solve the equation –x² + x – 2 = 0

Solve the equation x² + 3x + 5 = 0

Solve the equation `x^2 + x + 1/sqrt2 = 0`

Solve the equation  `sqrt2x^2 + x + sqrt2 = 0`

Solve the equation  `sqrt3 x^2 - sqrt2x + 3sqrt3 = 0`

Solve the equation  `x^2 + x/sqrt2 + 1 = 0`

Evaluate : `[i^18 + (1/i)^25]^3`

For any two complex numbers z₁ and z₂, prove that Re (z₁z₂) = Re z₁ Re z₂ – Im z₁ Im z₂

Reduce  `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.

If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`

Convert the following in the polar form:

`(1+7i)/(2-i)^2`

Convert the following in the polar form:

`(1+3i)/(1-2i)`

Solve the equation `3x^2 - 4x + 20/3 = 0`

Solve the equation   `x^2 -2x + 3/2 = 0`  

Solve the equation 27x² – 10x + 1 = 0

Solve the equation 21x² – 28x + 10 = 0

If z₁ = 2 – i,  z₂ = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`

If a + ib  = `(x + i)^2/(2x^2 + 1)` prove that a² + b² = `(x^2 + 1)^2/(2x + 1)^2`

Let z₁ = 2 – i, z₂ = –2 + i. Find Re`((z_1z_2)/barz_1)`

Let z₁ = 2 – i, z₂ = –2 + i. Find `Im(1/(z_1barz_1))`

Find the modulus  of  `(1+i)/(1-i) - (1-i)/(1+i)`

If (x + iy)³ = u + iv, then show that `u/x + v/y  =4(x^2 - y^2)`

If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a² + b²) (c² + d²) (e² + f²) (g² + h²) = A² + B².

if `((1+i)/(1-i))^m` =   1, then find the least positive integral value of m.