Complex Numbers

Numbers that has both real and imaginary parts are called complex numbers.It can be written as a + bi where a and b are real numbers and i is the standard imaginary unit.The standard imaginary number has the property i^2 = -1.

Complex numbers are useful abstract quantities that can be used in calculations and result in physically meaningful solutions.Unlike real numbers, complex numbers do not have a natural ordering, so there is no analog of complex-valued inequalities.

To assemble a complex number, a second number is associated with each real number.

A complex cardinal is again an ordered pair of absolute numbers (a,b).

We address that fresh cardinal as

a + bi

The '+' and the i are just symbols for now.

We call 'a' the absolute part and 'bi' the abstract part of the complex number.

Ex :

(2 , 4.6) or 2 + 4.6i ;

(0 , 5) or 0 + 5i ;

(-5 , 36/7) or -5 + (36/7)i 

Instead of 0 + bi, we address 5i.

Instead of a + 0i, we address a.

Instead of 0 + 1i, we address i.

The set of all complex numbers is C. 

Next time we will learn how to solve complex numbers problem like sum, product, multiplication, etc.