Hi guys, I'm stumped on this, and I was hoping someone could help me out - so here goes: Find all the complex numbers to the equation: 2|z| = |z-3-3i|.
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Originally Posted by takamura Hi guys, I'm stumped on this, and I was hoping someone could help me out - so here goes: Find all the complex numbers to the equation: 2|z| = |z-3-3i|. The locus is an Apollonian circle (but the geometric significance of the relation may not mean anything to you). Substitute : Calculate the magnitudes in the usual way. Then square both sides and simplify.
wrong work .. sorry . Thanks Prove it.
Last edited by mathaddict; Sep 25th 2009 at 10:58 PM.
Originally Posted by mathaddict Let and . SO ---1 and ----2 Now we have to solve the simultaneous equation From 1 , Substitute into 2 so when , and a will be the same . when , b=9 or b=-3 , so you can find a so you should get 4 different sets of z . PLs check through my algebra work . Should actually be . So the solution is the circle of radius units, centred at .
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