Infimum taken over $\lambda$ in $\mathbb{C}$ I want to calculate the infimum of 
$$ |\lambda-2|^2+|2\lambda-1|^2+|\lambda|^2 $$
over $\lambda\in\mathbb{C}.$
I choose $\lambda=2,1/2,0$ so that one term in the above expression becomes zeros and minimum comes out $5/2$ at $\lambda =1/2.$ Is this infimum also, please help.

Note that the given equation is the same as
$$|\lambda-2|^2+4|\lambda-\tfrac{1}{2}|^2+|\lambda^2|.$$
So we are looking for $\lambda$ to minimize the weighted sum of the distances to the points $2,\tfrac{1}{2},0\in\Bbb{C}$, with respective weights $1$, $4$ and $1$. This is the same as the weighted average of the points, which is
$$\frac{1}{1+4+1}(1\cdot2+4\cdot\tfrac{1}{2}+1\cdot0)=\frac{1}{6}(2+2)=\frac{4}{6}=\frac{2}{3}.$$
