A complex number may be defined as an ordered pair of real numbers and may be denoted by the symbol (a, b). If we write z = (a, b), then a is called the real part and b is called the imaginary part of z and may be denoted by Re(z) and Im(z) respectively.
Leonhard Euler was the first mathematician to introduce the greek symbol (read as iota) in or around 1977.
Mathematically, is equal to square root of -1, such that = -1. He also called this symbol as imaginary unit.
a) Every Real Number a can be written as a+i0. Therefore, every real number is considered as a Complex Number whose imaginary part is zero.
Thus the set of Real Numbers (R) is proper subset of Complex Numbers (C) such that RC.
b) A complex number z is said to be Purely Real if its imaginary part is ZERO i.e. Im(z) = 0 and Purely Imaginary if Real part is ZERO i.e. Re(z) = 0
c) ZERO (0) is purely imaginary as well as purely real i.e. z = 0+i0.
d) In case of Purely Imaginary Number, the real part must be zero and imaginary part may or may not be zero.
e) Every Real Number is Purely Real and every Purely Real number is a Real Number.
f) Every Imaginary Number may or may not be Purely Imaginary because Re(z) may or may not be zero.
g) ZERO (z = 0) is a Purely Imaginary Number which is not an Imaginary Number.