1. A complex number is also a number like other numbers,but the difference is that 'it is classified into two parts (Real part and imaginar part)"and the composition of two parts is called a complex number .
2. Mathematically, if 'a' and 'b' are two real numbers then the number of the form "z=a+bi " is called a complex number ,
Where "i " represents the imaginary quantity "iota " which is first invented by the great mathematician "Euler " .
The value of the imaginary quantity iota as i is given by the relation i=square root of negative one . (i = sq.(-1) ) .
By using the formulation of iota as "i "we can compute the algebra of iota "i " that is addition , subtraction,multiplication,division,powers of iota .......e.t.c
"Properties of iota"
1. The sum of four consecutive powers of iota =i is zero .
2. Use the power formula of iota for computing the largest power of iota
(i )^ 4n +m = (i ) ^ m
Remark :
1. Every Real numbers are complex numbers .
2.Every Complex number are not Real numbers .
3.finally , Every Real numbers are complex numbers but Every complex numbers are not Real numbers .
4.For every z = a + bi as a complex number
Real part of z = Re(z) = a
Imaginary part of z = Im (z) = b
5. A complex number is said to be purely real if the imaginary part of the complex number is zero .
That is , z is purely real if Im(z) =b=0
6. A complex number is said to be purely imaginary if the real part of the complex number is zero .
That is, z is purely imaginary if Re(z) =a=0
7. Composition of complex numbers are also a complex number .
Some examples of complex numbers
3 + 4i , 1 +i , i , i^i , -1/2 i ,1- i ,
Note that 5 is also a complex number because the number 5 can be written as
5 = 5 + 0i so , similarly every real number are complex numbers.
[ ] ( this was the first introduction for complex number )
[ ] Thank you *
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