FP2 1.0 / 5 MathematicsRevisionA2/A-levelEdexcel Created by: bigmdogCreated on: 16-05-14 15:01 Express the general term Ur of a series f(r) - f(r + 1) then [n_Σ_r=1 * Ur] = [n_Σ_r=1 * (f(r) - f(r + 1))] 1 of 6 A complex number can be expressed in three forms z = x+ iy Or z + r(cosθ +isinθ) Or z = re^iθ 2 of 6 De Moivre's theorem for z = r(cosθ + isinθ) z^n = [r(cosθ + isinθ)]^n = r^n[(cos(nθ) +isin(nθ)] 3 of 6 Express sin^n(θ) or cos^n(θ) in terms of of either cos(kθ) or sin(kθ) z + 1/z = 2cosθ Or z^n = 1/z^n = 2cos(nθ) Or z - 1/z = 2isinθ Or z^n - 1/z^n = 2isin(nθ) 4 of 6 Auxiliary equation for d^2y/dx^2 am^2 + bm + c = 0 5 of 6 General solution if the auxiliary equation has two real distinct roots (b^2 > 4ac) y = Ae^(αx) + Be(βx) 6 of 6

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