Edexcel AS Level Further Mathematics Core Pure Maths Formulae to Learn

Edexcel AS Level Further Mathematics Core Pure Maths Formulae to Learn i = - √-1 i² = - -1 Conjugate of z= a + bi - z*= a - bi If α and β are roots, the quadratic equation is... - z² - (α + β)z + αβ = 0 z = x + yi can be represented as the vector... - (x) (y) on the Argand diagram Modulus of z = x + yi - |z| = √x² + y² Argument of z = x + yi - tanθ = y/x (θ = arg) If z lies in first quadrant then arg z = - α If z lies in second quadrant then arg z = - π - α If z lies in third quadrant then arg z = - -(π - α) If z lies in fourth quadrant then arg z = - -α |z₁z₂| = - |z₁||z₂| |z₁/z₂| = - |z₁|/|z₂| arg(z₁z₂) = - arg (z₁) + arg (z₂) arg(z₁/z₂) = - arg (z₁) - arg (z₂) Circle radius r and centre z₁ = - |z - (z₁)| = r Perpendicular bisector between z₁ and z₂ - |z - z₁| = |z - z₂| Half line from z at angle θ = - arg (z - z₁) = θ Formula for the sum of the first n natural numbers is... - n ∑ r = ½ n (n + 1) r=1 To find the sum of a series that does not start at r = 1, use... - n ______ n_____ k-1 ∑f(r) = ∑ f(r) - ∑f(r) r=k___ r=1___ r=1 1/α + 1/β = - (α + β)/αβ 1/α + 1/β + 1/γ = - αβ + βγ + αγ/αβγ 1/α + 1/β + 1/γ + 1/δ = - αβγ + βγδ + γδα + δαβ/αβγδ Roots of a Cubic Polynomial: α + β + γ - -b/a Roots of a Cubic Polynomial: αβ + βγ +αγ - c/a Roots of a Cubic Polynomial: αβγ - -d/a Roots of a Quartic Polynomial: α + β + γ + δ - -b/a Roots of a Quartic Polynomial: αβ + αγ +αδ +βγ + βδ + γδ - c/a Roots of a Quartic Polynomial: αβγ + αβδ + αγδ + βγδ - -d/a Roots of a Quartic Polynomial: αβγδ - e/a α² + β² = - (α + β)² - 2αβ α² + β² + γ² = - (α + β + γ)² - 2(αβ + βγ + αγ) α² + β² + γ² + δ² = - (α + β + γ + δ)² - 2(αβ + αγ + αδ + βγ + βδ + γδ) α³ + β³ = - (α + β)³ - 3αβ(α + β) α³ + β³ +γ³ = - (α + β + γ)³ - 3(α + β + γ)(αβ + βγ + αγ) + 3αβγ