Sketch the graph of ; that is, find all which satisfy this equation. What geometric shape is it?

I don't know what to do here. Is it a circle?

My notes have steps in polar form:

...

I'm not sure how these were derived.

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- Sep 10th 2011, 06:17 AMterrorsquidTrying to sketch this graph on the complex plane
Sketch the graph of ; that is, find all which satisfy this equation. What geometric shape is it?

I don't know what to do here. Is it a circle?

My notes have steps in polar form:

...

I'm not sure how these were derived. - Sep 10th 2011, 06:24 AMsanderRe: Trying to sketch this graph on the complex plane
It is a circle with radius 4 and centre at .

- Sep 10th 2011, 06:29 AMterrorsquidRe: Trying to sketch this graph on the complex plane
- Sep 11th 2011, 01:35 AMandrew2322Re: Trying to sketch this graph on the complex plane
because y is the imaginary part, not iy, therefore you dont square i along with y.

it is a circle with radius 4 and center at (-5,0) as Sander pointed out - Sep 11th 2011, 04:34 AMHallsofIvyRe: Trying to sketch this graph on the complex plane
Sander and andrew2322 are using the fact that |z- a| is the distance from the point z to the point a in the complex plane. |z+ 5|= |z- (-5)| so |z+ 5|= 4 is satisfied for all points whose distanced from -5 is equal to 4- in other words, the circle with center -5 and radius 4.

Also, you arrived at and then proceeded to multiply out the square, etc. You should not have done that. You should have recognized immediately that this is of the form , the equation of a circle with center (a, b) and radius r, with a= -5, b= 0, and r= 4. - Sep 11th 2011, 08:33 AMterrorsquidRe: Trying to sketch this graph on the complex plane