# Complex Numbers

## Complex Numbers (Encyclopedia of Science)

Complex numbers are numbers that consist of two parts, one real and one imaginary. An imaginary number is the square root of a real number, such as 4;. The expression 4 is said to be imaginary because no real number can satisfy the condition stated. That is, there is no number that can be squared to give the value , which is what 4 means. The imaginary number 1 has a special designation in mathematics. It is represented by the letter i.

Complex numbers can be represented as a binomial (a mathematical expression consisting of one term added to or subtracted from another) of the form a + bi. In this binomial, a and b represent real numbers and i = 1. Some examples of complex numbers are 3 i, ½ + 7i, and 2i.

The two parts of a complex number cannot be combined. Even though the parts are joined by a plus sign, the addition cannot be performed. The expression must be left as an indicated sum.

History

One of the first mathematicians to realize the need for complex numbers was Italian mathematician Girolamo Cardano (1501576). Around 1545, Cardano recognized that his method of solving cubic equations often led to solutions containing the square root of negative numbers. Imaginary numbers did not fully become a part of mathematics, however, until they were studied at length by French-English mathematician Abraham De Moivre...

(The entire section is 862 words.)