Why doesn't a number similar to the imaginary number exist to make division by zero possible?

Suppose we want to solve the equation $1 = x \cdot 0$
Can't we assume a number similar to the imaginary number that is defined as a solution to this equation?
If we did that we would get $\frac{1}{u} = 0$ where u is our solution. We could use this to switch from the "imaginary" number space back to the real numbers similar to the complex numbers where $i^2 = -1$.
Tell me why I am retarded and why this doesn't work.