Once the reality of i as a number was accepted, mathematics was changed irrevocably. Instead of the numbers described by algebraic equations being points on a line, suddenly they become points on a plane. Algebraic numbers are really two-dimensional; and just like the integer 1 is the unit distance on the axis of the real numbers, i is the unit distance on the axis of the imaginary numbers. As a result numbers in general become what we call complex: they have two components, defining their position relative to those two axes. We generally write them as a + bi, where a is the real component and b is the imaginary component. You can see in the following figure what a complex number as a two-dimensional value means.

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