EE2111_A03_HW1

EE2111_A03_HW1 - 90 c) z c = 5 -120 d) z d = -3 45 Problem...

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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 . 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 . Problem 3 . Given z 1 = 4 - j3 and z 2 = - j5, determine z 1 + z 2 , z 1 - z 2 , z 1 z 2 , and z 1 /z 2 . Problem 4 . Express each of the following complex numbers in polar and in exponential form: a) z a = 4– j3 b) z b = -4 + j3 c) z c = -3 d) z d = - j3
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Problem 5 . Express each of the following complex numbers in rectangular form and in exponential form a) z a = 5 75 0 b) z b = -10
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Unformatted text preview: 90 c) z c = 5 -120 d) z d = -3 45 Problem 6 . Express each of the following complex numbers in rectangular form and in exponential form a) z a = 3 60 j e b) z b = - 10 45 j e c) z c = 15 45 j e d) z d = - 20 60 j e Problem 7 . Reduce each of the following to rectangular form a) z a = (1 + j2)( 3 45 ) b) z b = -3 -45 + 4 c) z c = 45 5 4 3 j d) z d = 2 2 90 6 j Problem 8 . Suppose that ( ) 1 45 cos 10 = t v and ( ) 2 30 sin 5 + = t v . Use phasors to reduce the sum ( ) ( ) ( ) t v t v t v s 2 1 + = to a single term of the form ( ) ( ) + = t V t v m s cos . Draw a phasor diagram showing V 1 , V 2 , and V s . State the phase relationships between each pair of these phasors. Problem 9 . Hambly P5.27 Problem 10 . Hambly P5.29...
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EE2111_A03_HW1 - 90 c) z c = 5 -120 d) z d = -3 45 Problem...

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