What Is a Complex Number in Standard Form?

By Staff WriterLast Updated Apr 8, 2020 5:07:26 PM ET

A complex number in standard form is a number that can be written as a + bi where a is the real number, b is the imaginary part and i is the imaginary unit that represents the square root of -1.

Besides standard form, a complex number can also be written in component notation, single letter notation or phasor form. In component notation, a + bi is written as (a, b), where a is the real number and b is the imaginary part. In single letter notation, a letter such as z represents the complex number. In phasor form, a complex number is written as |z|e^(i?) where |z| is the norm and ? is the complex argument. The norm is defined as the square root of the sum of the squares of a and b, while the complex argument is defined as the arctangent of b over a.