# geometry in complex numbers

#### sandy

Represent the following region in the complex plane by equations or inequalities in the variable​
z.

All the points outside a circle of radius 3, centered at x=-1, y=-2.

i drew the circle -4< x < 2 and -5<y<1

so how do we do the equation or the inequality?

#### Drexel28

MHF Hall of Honor
Represent the following region in the complex plane by equations or inequalities in the variable​
z.

All the points outside a circle of radius 3, centered at x=-1, y=-2.

i drew the circle -4< x < 2 and -5<y<1

so how do we do the equation or the inequality?
A circle of radius $$\displaystyle R$$ around a complex number $$\displaystyle z_0\in\mathbb{C}$$ is defined to be $$\displaystyle \left\{z\in\mathbb{C}:|z-z_0|=R\right\}$$

#### sandy

A circle of radius $$\displaystyle R$$ around a complex number $$\displaystyle z_0\in\mathbb{C}$$ is defined to be $$\displaystyle \left\{z\in\mathbb{C}:|z-z_0|=R\right\}$$
i didnt understand, the equation of a circle is |z-z_0|=R but how do we do the above as an inequality or equation?

#### Plato

MHF Helper
$$\displaystyle \left\{ {z:\left| {z - \left( { - 1 - 2i} \right)} \right| > 3} \right\}$$.

#### sandy

$$\displaystyle \left\{ {z:\left| {z - \left( { - 1 - 2i} \right)} \right| > 3} \right\}$$.
oh ok thankyou very much now i understood what they want and how to solve questions like that. thanks again