A complex number can be viewed as a point in the complex plane.

Complex plane is a modified Cartesian plane, where the real part of the complex number lies on x axis and the imaginary part lies on y axis.

The rectangular form of a complex number is usually called the algebraic form of the complex number.

z = x + y*i

x is the real part of the complex number z - Re(z)

y is the imaginary part of the complex number z - Im(z)

i = sqrt(-1)

The displacement of a point with respect to origin of the complex plane is called the modulus of the complex number:

|z| = sqrt[Re(z)^2 + Im(z)^2]

|z| = sqrt(x^2 + y^2)

The argument of a complex number is the angle made to real axis, x-axis.

tan a = y/x = Re(z)/Im(z)

The polar form of a complex number is:

z = |z|(cos a + i*sin a)