# Complex Conjugated Poles

Discussion in 'Homework Help' started by bserrato86, Apr 22, 2009.

1. ### bserrato86 Thread Starter New Member

Apr 18, 2009
2
0
So I'm studying for a test and I'm not sure how an answer was derived based on the previous number. Could someone tell me how the answer came about?

[10*(j1)] / [(-2+j1)*(j2)]

5 / [2.24 angle(153.43*)]

The final answer is in polar form but I don't get how it came about. I tried to solve it and it didn't work. Could someone show me the steps?

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I tried solving the bottom part by distribution:

(-4j + j^2 2) = (-2 - j4) = 4.47 angle(-63.43)

The top I didn't really know how it came to it. This part is of course part of the bigger problem but I don't understand how this part came about. I've included the slide I got it from & circled where I got stuck. Could someone help me understand?

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2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
Ignoring the (-2+j1) term for the moment you would have

(10*j1)/(j2)

The j terms in the numerator and denominator cancel and you are left with 10/2 or 5.

So re-introducing the (-2+j1) term in the denominator would give you

5/(-2+j1) and since (-2+j1) = √5 angle(153.43°) = 2.24 angle(153.43°)

you now have

5/(2.24 angle(153.43°)