Complex Numbers Part One
Complex Numbers part 1 Lets start with an example : Suppose you're told to solve the following equation and find the value of x^2+y^2: 1) (x+y)^2= -25 2) x y = -6 If you are smart you will say that it is impossible, supposing you don't know about complex numbers. But still you'll be able to solve it. so if it were incorrect it should have been impossible to find its root. But we have just done it. Well here is its story: In late 1500s, the master equation solver Girolamo Cardano was trying to solve polynomial equations. He had no trouble solving equations like x^2−8 x+12=0, because it was easy to find two numbers whose sum was 8 and whose product was 12: namely, 2 and 6. This meant x^2−8 x+12 could be factored as (x−2)(x−6), and expressing this polynomial as a product of two factors made solving the equation x^2−8 x+12=0 easy. But it wasn’t that easy to do this for equations like x^2-3 x+10=0. Finding two numbers that add to 3 and multiply to 10 seems an...