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Syllabus/Additional Topics in Math
04SAT Math

Complex Numbers

Complex Numbers

Definition

i = √(-1) | i² = -1 | i³ = -i | i⁴ = 1

Operations

  • Add/Subtract: combine real and imaginary parts separately
  • Multiply: use FOIL and replace i² with -1
  • Divide: multiply by conjugate of denominator
  • Conjugate

  • Conjugate of a + bi is a - bi
  • (a + bi)(a - bi) = a² + b² (always real)
  • SAT Tips

  • Powers of i cycle every 4: i, -1, -i, 1
  • To find i^n: divide n by 4 and use the remainder
  • Complex numbers appear in the "no real solutions" context
  • Complex Numbers | SAT Math Prep