Complex Numbers Practice _2

Complex Numbers Practice _2 - = − c 4 4 j j e j je × −...

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EE 301 HW#1 1. For each of the following complex numbers, show its graphical representation on the complex plane and convert it into polar form. a. 1- j b. 3 c. 4 j d. 2 10 j + e. –5- j 6 f. –3+ j 3 2. For each of the following complex numbers, show its graphical representation on the complex plane and convert it into rectangular form. a. 4 / 2 π j e b. j e 2 c. 3 / 5 j e d. 0 3 j e e. 3 / 2 2 j e f. 2 5 j e 3. Find the product of each of the pairs in 1 & 2 above (i.e., find the product of the # in 1a and the # in 2a: (1- j )* , etc.). 4 / 2 j e 4. Find the quotient of each of the pairs in 1 & 2 above (i.e., find the quotient of the # in 1a and the # in 2a: , etc.). 4 / 2 / ) 1 ( j e j 5. For each of the following complex numbers, simplify the result as appropriate (note: in each case the number is rewritten in a form that is helpful to find the answer) a. 4 / 4 / j j e j je × = b. 4 / 4 / 1 j j e e ×

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Unformatted text preview: = − c. 4 / 4 / j j e j je × − = − 6. For each of the following complex-valued sequences of numbers, plot the magnitude and phase versus the index } , 3 , 2 , 1 , , 1 , 2 , 3 , { … … − − − ∈ n . a. jn n z + = 5 ) ( b. jn n z + = 5 1 ) ( c. 2 2 1 ) ( j n n j n z + − = d. n j je n z jn 2 1 ) ( 10 / + = e. jn n j n z + = 1 ) sgn( ) ( , where ⎪ ⎩ ⎪ ⎨ ⎧ = < − > = for , for , 1 for , 1 ) sgn( n n n n 7. For each of the following functions, plot the magnitude and phase versus the variable . ) , ( ∞ −∞ ∈ x a. j x x z 5 10 ) ( + = b. ) sin( ) ( x x z = c. ) sin( ) sgn( ) ( x x j x z = d. x j e x z 2 ) ( = e. Plot the real and imaginary parts of the function in part d...
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This note was uploaded on 06/30/2010 for the course EECE 301 taught by Professor Fowler during the Fall '08 term at Binghamton.

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Complex Numbers Practice _2 - = − c 4 4 j j e j je × −...

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