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

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-Complex Algebra-

Complex numbers can undergo addition, subtraction, multiplication and division. Here are the basic rules:

  • Addition:

    (a+i.b) + (c+i.d) = (a+c) + i.(b+d)

  • Substitution:

    (a+i.b) - (c+i.d) = (a-c) + i.(b-d)

  • Multiplication:

    (a+i.b).(c+i.d) = (a.c - b.d) + i.(a.d + b.c)

  • Division:

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

    • In these cases a, b, c and d are real numbers and i is the squareroot of -1.