The division of two complex numbers is defined by the following formula: In particular, the square of the imaginary unit is −1: The multiplication of two complex numbers is defined by the following formula: For example, -3.5 + 2i is a complex number.Īddition of two complex numbers can be done geometrically by constructing a parallelogram.Ĭomplex numbers are added by adding the real and imaginary parts of the summands. Where a and b are real numbers and i is a mathematical symbol which is called the imaginary unit.
The idea is to enhance the real numbers by adding a number i whose square is −1, so that x = i and x = -i are the two solutions to the preceding equation.Ī complex number is an expression of the form Complex numbers are a solution to this problem. Has no real solution x, since the square of x is 0 or positive, so x^2 + 1 cannot be zero. The Chronicon Pictum (Latin for illustrated chronicle, English: Illuminated Chronicle or Vienna Illuminated Chronicle, Hungarian: Képes Krónika also referred to as Chronica Hungarorum, Chronicon (Hungariae) Pictum, Chronica Picta or Chronica de Gestis Hungarorum) is a medieval illustrated chronicle from the Kingdom of Hungary from the fourteenth century. In this way the complex numbers contain the ordinary real numbers while extending them in order to solve problems that would be impossible with only real numbers.Ĭomplex numbers have been introduced to allow for solutions of certain equations that have no real solution: Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part. A complex number is a number consisting of a real part and an imaginary part.
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