Complex number:

A number in the type of x + iy, where x, y are real numbers and i = √-1 is known as a complex number.

(i)   Normally for an integer n.

(ii)  If z = x + iy, then the real part of z is shown by Re (z) and the imaginary part denoted by Im(z).

(iii) A complex number is called purely real if  Im(z) = 0, and is called simply  imaginary if Re (z) = 0. The complex number 0 = 0 + i0 is both only real and only imaginary.

(iv) Two complex numbers are called similar if and only if their imaginary parts and real parts are separately same i.e. a + ib = c + id means a = c and b = d. but, there is no order relation in between complex numbers and the relation of the complex no a + ib < ( or > ) c + id are  meaningless.

(v)  Since a real number a may be defined as a + i.0, therefore each and every real number may be defined as a complex number whose imaginary part is zero. Therefore the set R of real numbers is a proper subset of the given complex numbers C.

Remark: Clearly for an integer n.

Representation of complex numbers in argand plane:

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