Complex Numbers Practice _4

Complex Numbers Practice _4 - a je-j π/2 write it in polar...

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EECE 301 Assigned 9/1/06 Fall 2006 Due 9/7/06 Prof. Fowler EE 301 HW#2 NOTE: Show Steps Used – don’t just use your calculator’s complex number functions!! 1. For each of the following complex numbers, show its graphical representation on the complex plane and convert it into polar form (show steps used – don’t just use your calculator’s rectangular-to- polar function). a. –4– j 3 b. 6 c. 3+2 e j π /4 d. –6 2. For each of the following complex numbers, show its graphical representation on the complex plane and convert it into rectangular form (show steps used – don’t just use your calculator’s polar-to- rectangular function). a. 4 e j π b. e j 0 c. 3 e j π /4 d. 2 e j 6 π 3. For each of the following complex numbers, write the result in the form indicated
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Unformatted text preview: a. je-j π /2 write it in polar form b. write it in rectangular form 4 / π j je − 4. For each of the following, write the result in polar form. a. (2+ j 3)/(–3+ j 2) b. (2+ j 3) × (–3+ j 2) c. 6 e j π /2 /3 e j π /4 d. (2 e j 6 π ) × (1+ j ) 5. Find an explicit expression for each of the following (by “explicit” I mean one that does not use “Re” or “Im” or “| . |” or “ ∠ ”): a. x ( t ) = Re{ e j ( ω t + π /2) }, t ∈ (-∞ , ∞ ) b. x ( t ) = Im{ e j ( ω t + π /2) } , t ∈ (-∞ , ∞ ) c. x [ n ] = 4 / ) 1 ( jn n e − , n = 1, 2, 3, … d. x [ n ] = { } 4 / ) 1 ( jn n e − ∠ , n = 1, 2, 3, … (Hint: write one expression for odd n & one expression for even n )...
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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 _4 - a je-j π/2 write it in polar...

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