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March 28th, 2017, 12:17 PM   #1
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complex number problem


I'm an Electrical Engineer and having difficulty wrapping my head around a phenomena I am experiencing when calculating short-circuit current. The problem boils down to:
Z1 = a1 + jb1
Z2 = a2 + jb2
Z3 = a3 + jb3

Z1mag > Z2mag
(Z1 + Z3)mag < (Z2 + Z3)mag

For what values of Z1, Z2, and Z3 should this occur? All values reside in the first quadrant (angles are greater than 0 and less than 90).

Last edited by chuckd83; March 28th, 2017 at 12:19 PM.
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March 28th, 2017, 06:55 PM   #2
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I've convinced myself it can't be done. Not if $z_3$ is in the first quadrant. Think of them as vectors. Put a representative of $z_3$ at the tip of each of $z_1$ and $z_2$. No value of $z_3$ will make the difference of the lengths of $z_1 + z_3$ and $z_2 + z_3$ change signs.

The only way you can get this to work is if $z_3$ is in some other quadrant. But I didn't work out a specific example.

I also convinced myself that as the length of $z_3$ gets larger, the two augmented lengths converge. But the sign never changes. The shorter one is always shorter.

I could be missing something obvious.

Last edited by Maschke; March 28th, 2017 at 06:58 PM.
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