A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the [quadratic] equation x 2 = −1. Because no real number satisfies this equation, i is called an imaginary number. For the complex number a + bi, a is called the real part, and b is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.
A complex number can be visually represented as a pair of
numbers (a, b) forming a vector on a diagram called an Argand diagram,
representing the complex plane. "Re" is the real axis, "Im" is the imaginary axis,
and i satisfies i
2 = −1
You can perform addition, subtraction, multiplication, and division for complex numbers
using the following formulas:
You can also obtain the absolute value for a complex number
using the following formula:
A complex number can be interpreted as a point on a plane by
identifying the (a, b) values as the coordinates of the point. So
you may think of complex numbers as two-dimensional
numbers, a superset of the real numbers. The absolute value of
the complex number, also called modulus or magnitude,
corresponds to the distance of the point to the origin.