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Unformatted text preview: Section 2.1 Complex Numbers The imaginary unit , , is defined as , where Ex . 7 7 1 7 i = = i 4 16 1 16 = = *Complex Numbers : can be written in the form , referred to as standard form a = “real part” b = “imaginary part” Ex . i + 3 i i 5 5 + = i 6 6 + = *Equality of Complex Numbers : di c bi a + = + if and only if c a = and d b = Ex . i i 3 5 2 3 7 + = + *Operations with Complex Numbers 1.) Adding : when adding two (or more) complex numbers, just add the real parts and add the imaginary parts EX 1 : EX 2 : ) 2 7 ( ) 4 ( ) 3 1 ( i i i + + + + 2.) Subtracting : i d b c a di c bi a ) ( ) ( ) ( ) ( + = + + EX 3: ) 7 3 ( ) 4 ( i i + + EX 4: ) 4 12 ( ) 6 2 ( i i + 3.) Multiplication : ) )( ( di c bi a + + use FOIL or distributive property EX 5: ) 9 2 ( 7 i i EX 6: ) 7 6 )( 4 5 ( i i + **Special case of Multiplication—Complex Conjugates EX 7: Multiply ) 2 1 )( 2 1 ( i i + The complex conjugate of the number bi a + is , bi a and vice versa. 2 2 2 2 ) )( ( b a b abi abi a bi a bi a + = + + = + 4.) Dividing – multiply the numerator and denominator by the complex conjugate of the denominator EX 8: Divide i i 3 4 4 3 + *Roots of Negative Numbers...
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This note was uploaded on 11/23/2010 for the course MATH 115 taught by Professor Mcbride,v during the Fall '08 term at University of South Dakota.
 Fall '08
 Mcbride,V
 Complex Numbers

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