Author Topic: Complex Numbers (Read 1060 times) Tweet Share

dejan91 · « **on:** March 21, 2009, 02:39:45 pm »

${z:|z+i|=3}}$

Can somebody please explain to me why the circle is translated down and not up?
Sorry for dumb question btw, I just can't seem to figure out why...lol.

Thanks

pHysiX · « **Reply #1 on:** March 21, 2009, 03:53:07 pm »

well i'm assuming you can convert that to cartesian form:

x^2 + (y+1)^2 = 9

Now do you see?

Damo17 · « **Reply #2 on:** March 21, 2009, 04:48:46 pm »

Standard equation of a circle is $(x-h)^2 + (y-k)^2 = r^2$ where h and k are the x- and y-coordinates of the centre of the circle and r is the radius.

so for ${z: \mid z+i \mid =3}}$
Convert to Cartesian:

$x^2+(y+1)^2=3^2$

but to look at translations we need it in the form $(x-h)^2 + (y-k)^2 = r^2$ so now you can state it as:
$<br />x^2+(y-(-1))^2=9$

That $-1$ means the circle is translated down 1 unit (imaginary axis) from the base circle graph of $x^2 + y^2=r^2$ .

dejan91 · « **Reply #3 on:** March 21, 2009, 05:05:01 pm »

Oh ok cool thanks for that.
I forgot the cirlce equation and couldn't figure out why lol.

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