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: 
$\{1,i\}$ is a basis for complex numbers $\Bbb C$ as a vector space over real numbers $\Bbb R$; the dimension is $2$. 

A basis for $\Bbb C^2$ as a vector space over $\Bbb R$ is $\{(1,0), (i,0), (0, 1), (0,i)\};$ the dimension is $4$. 

In general, a complex vector space of dimension $n$ is a real vector space of dimension $2n$.
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.