
Argument
The angle created by the positive real axis and the segment connecting the origin to the plot of a complex number in the complex plane.

Complex Conjugate
The complex conjugate of a given complex number a + bı is a  bı.

Complex Number
The set of all numbers of the form a + bı, where a and b are real numbers. The real numbers are all complex numbers.

Complex Plane
A plane with two perpendicular axes, the real axis and the imaginary axis, on which a complex number a + bı is plotted at the coordinate (a, b). It is customary for the real axis to coincide with the xaxis of the rectangular coordinate system, and for the imaginary axis to coincide with the yaxis of the rectangular coordinate system.

Imaginary Axis
The axis in the complex plane that customarily coincides with the yaxis of the rectangular coordinate system, and on which the imaginary part bı of the complex number a + bı is plotted.

Imaginary Number
A number that can be expressed in the form bı, where b is a real number.

Imaginary Part
The bı term in every complex number a + bı.

Imaginary Unit
The imaginary unit is ı. ı = .

Modulus
for a complex number a + bı. In the complex plane, it is the distance between the plot of a complex number and the origin.

Polar Form of a Complex Number
The polar form of a complex number z = a + bı is this: z = r(cos(θ) + ısin(θ)), where r =  z and θ is the argument of z.

Real Axis
The axis in the complex plane that typically coincides with the xaxis of the rectangular coordinate system, and on which the real part a of a complex numbers a + bı is plotted.

Real Part
In a complex number a + bı, a.

Standard Form
For a complex number, a + bı.
Terms
Formulae
De Moivre's Theorem  Let z = r(cos(θ) + ısin(θ).Thenz^{n} = [r(cos(θ) + ısin(θ)]^{n} = r^{n}(cos(nθ) + ısin(nθ), where n is any positive integer. 
Roots of a Complex Number  A complex number z = r(cos(θ) + ısin(θ) has exactly nnth roots given by the equation [cos() + ısin()], where n is a positive integer, and k = 0, 1, 2,..., n  2, n  1. 