How would I do this?
I know it's a circle of radius half around 3 and a larger circle of radius 1 around 3. But why?
How would I do this?
I know it's a circle of radius half around 3 and a larger circle of radius 1 around 3. But why?
With complex numbers, $|a-b|$ will give you the distance between $a$ and $b$. Hence $$|2z-6|=2|z-3|$$ is twice the distance from $z$ to $3$. Divide your inequalities by $2$, and you get $${1\over 2}<|z-3|\leq 1$$ In other words, the distance between $z$ and $3$ should lie between $1\over 2$ and $1$, which is the same as the answer you gave.