5. COMPLEX NUMBERS

A complex number is a NUMBER that can be expressed in the form a + bi, where a and b are Real numbers and i is the Imaginary unit that satisfies the equation x² = −1, that is, i² = −1.^[1] In this expression, a is the real part and b is the imaginary part of the complex number. The complex number a + bi can be identified with the point (a, b) in the complex plane

A Complex Number is a combination of a Real Number and an Imaginary Number

 Imaginary number:

The ordered pair (0, 1) is denoted by the letter i , read as “IOTA”. Then , i² = i.i

= (0, 1) . (0, 1)

= (-1, 0) ∈ Complex

= -1 ∈ R

so .i= √-1.

“i”  is called an imaginary number because there is no real number x satisfying the property  x² = -1.

The number of  the form  ib   is called an imaginary number,∀b ∈ R.