Solving Equations with Complex Roots (Edexcel A-Level Further Mathematics): Flashcards

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Solving Equations with Complex Roots
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Formula for discriminant

Δ=b2−4ac\Delta = b^2 - 4ac

Discriminant > 0 means roots are...

Real and distinct

Discriminant = 0 means roots are...

Real and equal

Discriminant < 0 means roots are...

Complex conjugates

Quadratic formula

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Complex roots always occur as...

Conjugate pairs

Value of i2i^2

−1-1

If z=a+biz = a + bi, then z‾=?\overline{z} = ?

a−bia - bi

Form of roots when Δ<0\Delta < 0

x=a±bix = a \pm bi

Roots of x2+4x+5=0x^2 + 4x + 5 = 0

x=−2±ix = -2 \pm i

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