Like real numbers, imaginary numbers are a subset of the set of all. Imaginary numbers are typically represented as either the constant i (in mathematics) or j (in engineering and the sciences), where i² = -1 or sqrt(-1) = i. Like the real numbers, imaginary numbers have relative magnitude and can be plotted along a number line, with 3i > i. Imaginary numbers may also be negative, with 3i > i > -i > -3i. Any imaginary number ki can be written as the complex number 0 + ki.

Properties of Imaginary Numbers

Imaginary numbers follow the same rules of addition and subtraction available to real numbers. For example, 3 + 2 = 5 and 4 - 6 = -2 in the real number plane. Similarly, 3i + 2i = 5i and 4i - 6i = -2i in the imaginary number plane. Note, however, that 3 + 3i ( 6, as 3 = 3 * sqrt(1) and 3i = 3 * sqrt(-1), which are not equal.

Scalar multiples of imaginary numbers...