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EE2111_A03_SOL1

EE2111_A03_SOL1 - EE2111 Homework#1 A03 Assigned 28 August...

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EE2111 Homework #1 A03 Assigned 28 August 03 Due 3 September 03 Practice with Complex Number Manipulation Remember: Complex numbers can be expressed in rectangular, polar or exponential forms. Addition, subtraction, multiplication and division of complex numbers are necessary operations for solving steady-state ac circuits by the phasor method. Problem 1 . Given z 1 = 1 + j3 and z 2 = -2 + j2, determine z 1 + z 2 , z 1 - z 2 , z 1 z 2 , and z 1 /z 2 . Solution: ( )( ) ( )( ) ( )( ) j j j j j j j j j j z z j j j j j z z j j j z z j j j z z = = + = + + = + + = = + = + + = + = + + = + = + + = + 2 1 8 8 4 8 6 6 2 2 2 2 2 2 2 2 3 1 2 2 3 1 4 8 6 6 2 2 2 2 3 1 1 3 2 2 3 1 5 1 2 2 3 1 2 1 2 1 2 1 2 1
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Problem 2 . Given z 1 = 1 + j2 and z 2 = 3 - j2, determine z 1 + z 2 , z 1 - z 2 , z 1 z 2 , and z 1 /z 2 . Solution: ( )( ) ( )( ) ( )( ) 13 8 13 1 13 8 1 13 4 6 2 3 2 3 2 3 2 3 2 1 2 3 2 1 4 7 4 6 2 3 2 3 2 1 4 2 2 3 2 1 4 2 3 2 1 2 1 2 1 2 1 2 1 j j j j j j j j j j z z j j j j j z z j j j z z j j z z + = + = + + = + + + = + = + = + + = + = + = + + = = + + = + Problem 3 . Given z 1 = 4 - j3 and z 2
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