imaginary number
imaginary numberA number (symbol i) whose square equals a real negative number. Imaginary numbers were invented to allow equations to be solved when they have no real roots. For example, 1 has two real square roots, +1 and −1. The equation x2 = 1 thus has two real roots, x = 1 and x = −1. The number −1 has no real square roots, so the equation x2 = −1 has no real roots. However, the ‘imaginary’ number, denoted by i, allows the equation x2 = −1 to have two imaginary roots, x = i and x = −i. By convention i always precedes any coefficient other than 1 or −1.
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