REVIEW OF COMPLEX NUMBERS:
Introduction :
- Mathematician L.Euler named a number 'i' as Iota whose square is -1 ie i=√-1 .This Iota or i is defined as imaginery unit.
- It is because of i ,we can interpret the square root of a negative number as a product of a real number with i. example. √-9 =3i
Defination :
Any number that can be written in the form of a+ bi where a,b are real numbers and i=√-1 is called a complex number.
Operations :
- Addition:(a + bi) + (c + di) = (a + c) + (b + d)i
- Subtraction:(a + bi) - (c + di) = (a - c) + (b - d)
- Multiplication:(a + bi) (c + di) = ac + bci + adi + bd i^2 = (ac - bd) + (bc + ad)
- Division: (a + bi)}{(c + di)} = \left({ac + bd \over c^2 + d^2}\right) + \left( {bc - ad \over c^2 + d^2} \right)i\, where c and d are not both zero.
