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March 28th, 2017, 12:17 PM  #1 
Newbie Joined: Mar 2017 From: Houston Posts: 1 Thanks: 0  complex number problem
Hi, I'm an Electrical Engineer and having difficulty wrapping my head around a phenomena I am experiencing when calculating shortcircuit 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. 
March 28th, 2017, 06:55 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,973 Thanks: 551 
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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