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Quadratics with complex roots

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Useful for: IB Math AA HL AP® Precalculus

Learn it When b² − 4ac < 0, the quadratic formula gives complex roots: x = (−b ± i√(4ac − b²))/2a. They come in conjugate pairs p ± qi.

Example: Solve x² − 4x + 13 = 0.

  1. D = 16 − 52 = −36.
  2. x = (4 ± 6i)/2 = 2 ± 3i.

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