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Complex Review

Complex Review - REVIEW OF COMPLEX NUMBERS The Imaginary...

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REVIEW OF COMPLEX NUMBERS The Imaginary Number i : 2 1 1 i and i - = = - Complex numbers are always written in the form a + bi ( a is the real part and b is the imaginary part) Examples : Write as complex numbers. a) 25 - = 25 1 25 1 25 5 i - = - = - = b) 17 - = 17 1 17 1 17 17 i - = - = - = c) 9 - - = ( 29 ( 29 ( 29 9 1 9 1 9 3 3 i i - - = - - = - - = - = - d) (2 3 ) ( 4 6 ) i i + + - + = 2 3 4 6 2 4 3 6 2 9 i i i i i + + - + = - + + = - + e) (6 10 ) (9 3 ) i i - + - = 6 10 9 3 6 9 10 3 15 13 i i i i i - + - = + - - = - f) (6 4 ) ( 2 6 ) i i + - - + = (6 4 ) ( 2 6 ) 6 4 2 6 8 2 i i i i i + - - + = + + - = - g) (2 ) (3 10 ) i i + - + = (2 ) (3 10 ) 2 3 10 1 9 i i i i i + - + = + - - = - - h) (8 3 )(1 2 ) i i + + = 2 8 16 3 6 8 19 6 8 19 2 ( 1) 6 19 i i i i i i + + + = + + = + - = + - i) 3 (5 6 ) i i - = 2 15 18 15 18 15 18 18 15 ( 1) i i i i i - - = - = + = + The conjugate of a + bi is a bi . Examples : Find the conjugate of the following complex numbers. a) 2 + 6 i 2 – 6 i b) –3 – 4 i –3 + 4 i c) 15 i –15 i

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To divide two complex numbers, multiply the numerator and denominator by the conjugate of the denominator. Examples : Divide. Be sure to write each answer in standard form. a) 5 5(2 ) 2 (2 )(2 ) 10 5 2 2 2 4 2 5 i i i i i i i i i - - - = ° + + - - = - = + 2 i + 2 10 5 4 ( ) 10 5 5 5 5 1 10 5 2 i i i i i - - = - - = = - = - - b) 2 1 4 (1
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Complex Review - REVIEW OF COMPLEX NUMBERS The Imaginary...

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