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    Definition

    Real numbers have a property specifying that for any real number r,

    r ² > 0

    Complex number is an extention of the real numbers, adding a number i satisfying the equation i ^ 2 = -1

    A complex number is usually written in the form: a + bi

    a and b are real numbers, a being call the real part, and b the imaginary part.

    Two complex numbers a + bi and c + di are considered equal if :
    a=c AND b=d

    Operations

    Addition

    Adding two complex numbers is simply done by adding the real parts together and the imaginary parts together.

    (a+bi) + (c+di) = (a+b) + (c+d)i

    + (Complex)

    Subtraction

    Subtracting two complex numbers is simply done by adding the real parts together and the imaginary parts together.

    (a+bi) - (c+di) = (a-b) + (c-d)i

    - (Complex)

    Multiplication

    To process multiplication, we use standard algebra rules:

    (a + bi) * (c + di) = (ac - bd) + (ad + bc)i

    decomposition:
    (a + bi) * (c + di) = ac + adi + c * bi + bi * di = ac + (ad + bc)i + bd i² = (ac - bd) + (ad + bc)i

    * (Complex)

    Division

    (a + bi) / (c + di) = ( (ac + bd + (bc - ad)i ) / (c² + d²)

    / (Complex)

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