A number with both a real and an imaginary part, for example (a + ib), where a and b are real numbers and i is defined as the square root of -1. The sum, difference, product, and ratio of any pair of complex numbers are themselves complex numbers. For any two complex numbers (a + ib) and (c + id), (a + ib) + (c + id) = (a + c) + i(b + d),(a + ib) - (c + id) = (a - c) + i(b - d),(a + ib)(c + id) = (ac - bd) + i(bc + ad), and(a + ib)/(c + id) = [(a + ib)(c - id)]/[(c + id)(c - id)] = [(ac + bd)/(c² + d²)] + i[(bc - ad)/(c² + d² )]. In each case it is possible that for the particular values of a, b, c and d chosen the real or the imaginary part of the resulting complex number may be zero.

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