TOPICS

Formulae

Complex Numbers And Quadratic Equations

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

1. (z₁ + z₂)^{2}= z₁^{2}+ 2 z₁.z₂ + z₂^{2}2. (z₁ - z₂)^{2}= z₁^{2}- 2 z₁.z₂ + z₂^{2}3. (z₁ + z₂)^{3}= z₁^{3}+ z₂^{3}+ 3 z₁^{2}.z₂ + 3 z₁.z₂^{2}4. (z₁ - z₂)^{3}= z₁^{3}- z₂^{3}- 3 z₁^{2}.z₂ + 3 z₁.z₂^{2}5. z₁^{2}- z₂^{2}= (z₁ + z₂)(z₁ - z₂)

1. The conjugate of the complex number z = a + ib, denoted byz, is given byz= 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

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