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Subject:  Precalculus

Divide (1 + i) / (1 − i)

Multiply numerator and denominator by the conjugate to divide two complex numbers.

Answer i

Solution

  1. Inputs z₁ = 1 + i, z₂ = 1 − i
  2. Multiply by conjugate denominator becomes c² + d² = 2
  3. Real part (ac + bd)/2 = 0
  4. Imag part (bc − ad)/2 = 1
  5. Result i
  6. Modulus |z| = √(re² + im²) = 1

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