Terms
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.
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.
