This is the answer to a common question about why we need to define the square root of -1 at all.

Well the answer rests on the fact that you want all algebraic equations to be solvable. If you consider the set of all real numbers, equations such as

x ^{ 2 } + 3 = 5
can be solved. The solution above is of course sqrt(2).

However if you want *all * algebraic equations to be solvable the real number system is insufficient. For example the equation:

x ^{ 2 } + 1 = 0
does not have a real

solution. It turns out that the only addition you need to make to the

real number system is to introduce this funny quantity called

** i ** and say that numbers of the form

** a + i*b ** are to be called complex numbers. With this addition

** every ** algebraic equation is solvable.