﻿ Class 11 NCERT Math Solution
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TOPICS
Formulae
Algebra of Complex Numbers :-
```1. Addition of two complex numbers : z₁ + z₂
2. Difference of two complex numbers : z₁ - z₂
3. Multiplication of two complex numbers : z₁ . z₂
4. Division of two complex numbers : z₁/z₂
5. Power of i : i = √-1, i² = -1, i³ = -i, i⁴ = 1 etc.
6. The square roots of a negative real number : √-a = √a √-1 = √a i
```
Identities of Complex Numbers :-
```1. (z₁ + z₂)2 = z₁2 + 2 z₁.z₂ + z₂2
2. (z₁ - z₂)2 = z₁2 - 2 z₁.z₂ + z₂2
3. (z₁ + z₂)3 = z₁3 + z₂3 + 3 z₁2.z₂ + 3 z₁.z₂2
4. (z₁ - z₂)3 = z₁3 - z₂3 - 3 z₁2.z₂ + 3 z₁.z₂2
5. z₁2 - z₂2 = (z₁ + z₂)(z₁ - z₂)
```
Polar form of Complex Numbers :-
```1. The conjugate of the complex number z = a + ib, denoted by z , is given by z = a – ib
2. The modulus of the complex number z = a + ib, denoted by |z| or r , is given by r = √x² + y²
3. The polar form of the complex number z = x + i y is r(cosθ + i sinθ), where r = √x² + y² (the modulus of z) & cosθ = x/r, sinθ = y/r.
```
```1. The solutions of the quadratic equation ax² + bx + c = 0, where a, b, c ∈ R, a ≠ 0, b² – 4ac < 0, are given by