Plotting the set $\left\{ z\in \mathbb{C} : \left| z+i \right| =2\left| z \right| \right\} $ I have a question which can be simple, though I couldn't catch the idea.
Consider the Set given below:
$$E=\left\{ z\in \mathbb{C} : \left| z+i \right| =2\left| z \right|  \right\} $$
I have to find its graph to plot.
The Answer is the following: the Set $E$ is a circle, centred at $i/3$ and of radius $2/3$
I was not able of visualizing this set, I absurdly thought about a spiral. Any calculations neither didn't lead me to a solution. And especially, my conclusion was that this graph couldn't be a circle at all.
Thanks for helping me in advance.

Hint 
Put $z=x+yi$ in given equation to get $$x^2+(y+1)^2=4(x^2+y^2)$$
$$\Rightarrow 3(x^2+y^2)-2y-1=0$$
$$\Rightarrow x^2+y^2-\frac 23 y-\frac 13=0$$
Which is the equation of required circle with centre $(0,\frac 13)$ and radius $\frac 23$ but since we are dealing in complex plane the centre is $\frac i3$
