Activity 9

Activity 9 - 1 )( x-c 2 ) ( x-c n ) where a, c 1 , c 2 , ....

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Activity 9 Name Theorem on Algebra We defne the imaginary unit i = - 1. Further, given two real numbers a and b , the number a + bi is a complex number . 1. Add or subtract the ±ollowing complex numbers. a) (3 + 2 i ) + (4 - 1 3 i ) b) (3 + - 8) - (4 - - 2) 2. Multiply the ±ollowing complex number. a) (3 + 2 i )(4 - 1 3 i ) b) (3 + - 8)(4 - - 2) 3. Factor the ±ollowing polynomials (using complex solutions): a) f ( x ) = x 2 - 3 x + 4 b) h ( t ) = 2 t 2 - 2 t + 3 (Notice how complex ±actors always come in pairs call conjugate pairs .)
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The Fundamental Theorem of Algebra If f ( x ) is a polynomial of degree n , then f ( x ) has precisely n factors in the complex numbers and may be written as f ( x ) = a ( x - c
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Unformatted text preview: 1 )( x-c 2 ) ( x-c n ) where a, c 1 , c 2 , . . . , c n are complex numbers. 4. Factor the following polynomials (using complex solutions): a) f ( x ) = x 3-3 x 2 + 4 x b) h ( t ) = 2 t 4-2 t 3 + 3 t 2 5. Find a polynomial with real coecients that has the given zeros: a)-2 , 1 + 8 i, 1-8 i b) 3 , 4 ,-6 i 6. Find a polynomial with the following properties: a) f (-2) = 0 , f (2) = 0 , f (0) = 8 , degree= 2 b) f (-2) = 0 , f (2) = 0 , f ( i ) = 0 , f (0) = 1 , degree= 4 7. Find the equations for the following two functions. a) b)-4-2 2 4-4-2 2 4-2-1 1 2 3-10-5 5...
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Activity 9 - 1 )( x-c 2 ) ( x-c n ) where a, c 1 , c 2 , ....

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