Question: Let's consider the following problem. Imagine there is a tank filled up water (it's volume is equal to $V$). We connect two pumps to out tank. The first one pumps into the tank a mixture of 10% alcohol and water ($s\_1$ liter per minute). The second one pumps out of the tank what's inside (with the speed equal to $s\_2$ liters per minute).

I am to find the function $x(t)$ which describes the concentration of alkohol in a tank at any given time $t$. Of course $x(0) = 0$.

I am a bit stuck here. How should the equation look like? How can I derive it?

Answer: 
In general you can prove the following:

Let $V$ be a vector space over $\mathbb{C}$ of dimension $\text{dim}\_{\mathbb{C}}(V) = n$. If you choose a basis $v\_1,\dots, v\_n \in V$ of $V$ as a $\mathbb{C}$-vector space, then $v\_1,\dots, v\_n,iv\_1,\dots, iv\_n \in V$ is a basis of $V$ as a $\mathbb{R}$-vector space. That means we have $\text{dim}\_{\mathbb{R}}(V) = 2n$. You can apply that to your situation.
Since C² = C x C = R² x R² = R x R x R x R

=> C² has 4 unit vectors

=> Base has 4 Elements

=> dimension of the R-vector space of (C²) = 4.