Quadratic Equations With Complex Roots (Leaving Cert Mathematics): Flashcards

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Quadratic Equations With Complex Roots
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Condition for complex roots (discriminant)

b2−4ac<0b^2 - 4ac < 0

The discriminant of ax2+bx+c=0ax^2 + bx + c = 0

b2−4acb^2 - 4ac

Quadratic formula for ax2+bx+c=0ax^2 + bx + c = 0

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

Standard form of complex numbers

a+bia + bi

What ii represents

−1\sqrt{-1}

Value of i2i^2

−1-1

Real part in a+bia + bi

aa

Imaginary part coefficient in a+bia + bi

bb

If one root is a+bia + bi, the other root is

a−bia - bi (conjugate pair)

Variable used for complex roots instead of xx

zz

What −4\sqrt{-4} simplifies to

2i2i

If 2+3i2 + 3i is a root, the other root is

2−3i2 - 3i

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