5	Portent of the ideal world The Square Root of Minus One

What does it say?

Even though it ought to be impossible, the square of the number i is minus one.

Why is that important?

It led to the creation of complex numbers, which in turn led to complex analysis, one of the most powerful areas of mathematics.

What did it lead to?

Improved methods to calculate trigonometric tables. Generalisations of almost all mathematics to the complex realm. More powerful methods to understand waves, heat, electricity, and magnetism. The mathematical basis of quantum mechanics.