Complex Numbers
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 Introduction
Argand Diagrams
Complex Algebra
De Moivre's Theorem
Complex Conjugates

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-Complex Conjugates-

Complex conjugate is just a complex number with every i being replaced by -i. So z = a + i.b has a complex conjugate z* = a - i.b. Complex conjugation is a reflection in the real axis of an argand diagram.

There are some useful identities involving conjugates:

  • (z1.z2)* = z1*.z2*
  • (z1 + z2)* = z1* + z2*
  • (z1*)* = z1

    • Complex conjugates are useful for complex division. z1 ÷ z2 can be solved by multiplying by z2* ÷ z2*. Taking z1 as a + i.b and z2 as c +i.d gives the result shown on the algebra page:

    (a+i.b) ÷ (c+i.d) = [(a.c + b.d) + i.(b.c - a.d)] / (c2 - b2)