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| − | REVIEW OF COMPLEX NUMBERS: | + | '''REVIEW OF COMPLEX NUMBERS:''' |
| − | Introduction : | + | '''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. | - 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. | ||
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| − | + | ''' | |
| − | Defination : | + | 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. | 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 and Examples : | + | '''Operations and Examples :''' |
| − | - Addition:(a + bi) + (c + di) = (a + c) + (b + d)i. for example | + | - ''Addition'':(a + bi) + (c + di) = (a + c) + (b + d)i. for example |
( 3 + 4i ) + (5 + 6i ) = ( 3+5) + (4 +6) i = 8 + 10i | ( 3 + 4i ) + (5 + 6i ) = ( 3+5) + (4 +6) i = 8 + 10i | ||
| − | - Subtraction:(a + bi) - (c + di) = (a - c) + (b - d).for example | + | - ''Subtraction'':(a + bi) - (c + di) = (a - c) + (b - d).for example |
( 3 + 4i ) - (5 + 6i ) = ( 3-5) + (4 -6) i = -2 - 2i | ( 3 + 4i ) - (5 + 6i ) = ( 3-5) + (4 -6) i = -2 - 2i | ||
| − | - Multiplication:(a + bi) (c + di) = ac + bci + adi + bd i^2 = (ac - bd) + (bc + ad).for example | + | - ''Multiplication'':(a + bi) (c + di) = ac + bci + adi + bd i^2 = (ac - bd) + (bc + ad).for example |
(3+ 4i) (5 + 6i) = 15 + 20i +18i + 24 i^2 = -9 + 38i | (3+ 4i) (5 + 6i) = 15 + 20i +18i + 24 i^2 = -9 + 38i | ||
Revision as of 19:59, 4 September 2008
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 and Examples :
- Addition:(a + bi) + (c + di) = (a + c) + (b + d)i. for example
( 3 + 4i ) + (5 + 6i ) = ( 3+5) + (4 +6) i = 8 + 10i
- Subtraction:(a + bi) - (c + di) = (a - c) + (b - d).for example
( 3 + 4i ) - (5 + 6i ) = ( 3-5) + (4 -6) i = -2 - 2i
- Multiplication:(a + bi) (c + di) = ac + bci + adi + bd i^2 = (ac - bd) + (bc + ad).for example
(3+ 4i) (5 + 6i) = 15 + 20i +18i + 24 i^2 = -9 + 38i
