The locus of the points (x,y) satisfying the relationship

|z| = 2|z-1|

is

A region exterior to a circle

or

A region interior to a circle

or

A circle

many thanks

ck

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- Oct 10th 2009, 04:38 AMChris0724locus points
The locus of the points (x,y) satisfying the relationship

|z| = 2|z-1|

is

A region exterior to a circle

or

A region interior to a circle

or

A circle

many thanks

ck - Oct 10th 2009, 05:22 AMHallsofIvy
If z= x+ iy, then $\displaystyle |z|= \sqrt{x^2+ y^2}$ and $\displaystyle |z- 1|= \sqrt{(x- 1)^2+ y^2}$ so your equation says that $\displaystyle \sqrt{x^2+ y^2}= 2\sqrt{(x-1)^2+ y^2}$. Square both sides of that and reduce. What figure is that?

But with "multiple choice" you should be able to look at that equation and get the answer simply by the fact that it**is**and equation! - Oct 10th 2009, 06:52 AMChris0724
- Oct 10th 2009, 02:20 PMmr fantastic