Complex number

Number with a real and an imaginary part

In mathematics, a complex number is a number of the form ⁠ a + b i {\displaystyle a+bi} ⁠, where a and b are real numbers, and i is the imaginary unit, a number that satisfies the equation ⁠ i 2 = − 1 {\displaystyle \textstyle i^{2}=-1} ⁠; the number a is called the real part of ⁠ a + b i {\displaystyle a+bi} ⁠, and b is called the imaginary part. The complex numbers form a number system which extends the real numbers and supports the same basic arithmetic operations of addition, subtraction, multiplication, and division, satisfying the same associative, commutative, and distributive laws. This makes the complex numbers a field.

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