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)