I was doing some simple exercises with vectors and I wondered what the inverse of lets say the vector $\vec v = \vec i + \vec j $ is.
I multiplied with the denominator and numerator with $\vec w = \vec i - \vec j$, but realized the denominator becomes zero.
I used Geogebra to see what will happen if I do this. The thing is when a vector is inverted, the result is a complex number. Why is this so?