Finding a neighbourhood of $1/2 + i/4$ contained entirely in $\{z \in \Bbb C :|z-i|<1\}$ 
Consider the open set $\{z \in \mathbb{C}: |z-i|<1\}$. Write down an explicit formula for a neighbourhood of $1/2 + i/4$ contained entirely in the open set. 

I am not sure on how to complete this problem. 
I tried using the equation to a circle. 

Try thinking of $\mathbb{R^2}$ instead of $\mathbb{C}$. Making a sketch should help.
