Complex numbers

**usagi_killer** · October 17th 2009, 09:30 PM

Show that $\mid z-2i\mid = 4-z$ can be represented by the cartesian equation $\frac{x^2}{3}+\frac{(y-1)^2}{4}=1$

**mr fantastic** · October 17th 2009, 10:01 PM

Originally Posted by usagi_killer

Show that $\mid z-2i\mid = 4-z$ can be represented by the cartesian equation $\frac{x^2}{3}+\frac{(y-1)^2}{4}=1$

You're missing magnitude brackets on the right hand side of the relation: it should be |4 - z|. Furthermore, the locus of |z - 2i| = |4 - z| is NOT a circle so the result you're trying to prove is wrong.

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