Hi, I would like to know if there is a quick way to deducing the locus of points of the following, where z is a complex number.(adsbygoogle = window.adsbygoogle || []).push({});

(i) |z-1| + |z+3| = 4

(ii) |z+1| - |z-4| = 2

I know that the first one is an ellipse and the second one is a hyperbola (if I remember correctly anyway) since there is a plus in the first one and a minus in the second one.

I'm looking for a general method or observation which I can use to quickly deduce whatt he locus is(assuming that such a method exists). For example |z - (a+bi)| < c is a circle with centre (a,b) and radius c.

Any help would be good thanks.

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# Deduce the locus of points of the following equation

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