Mathematics - Complex Analysis - Complex numbers - What's √(-1)?

Scenario: Solve x²+1=0. x²=-1. x=√(-1). But no real number squared gives -1! Branch 1: 'Give up - no solution.' Branch 2: 'Invent a new number!' Choose Branch 2. Meet i, where i²=-1. Now x²+1=0 has solutions: x=i and x=-i. 'By inventing ONE new number, we can solve EVERY polynomial equation!' Show h