Division Using Conjugates

Complex Analysis · Axiom Academy

EXAMPLE Division Using Conjugates Divide complex numbers by multiplying through by the conjugate of the denominator. Evaluate the quotient and express the answer in standard form a + bi . Nice work. You divided two complex numbers by clearing the imaginary part out of the denominator. Use the conjugate: to divide by c + di , multiply the numerator and denominator by its conjugate c - di . The denominator becomes real: (c+di)(c-di) = c^2 + d^2 , which is exactly |c+di|^2 — always a real number. Result: , which is 2.2 - 0.4i . The same conjugate trick that rationalizes a radical denominator also "realizes" a complex one.

This is the written version of the interactive lesson above. See the full Complex Analysis course.