When I was in middle school, I was always puzzled why those mathematicians would invent complex, irrational number, negative number on top of positive number. Why bother and make the route to grasp math more difficult?
I took some research on Euler equation, the famously most elegant one
I am amazed by and greatly interested in the interconnection, necessity and importance of these inventions.
We know Taylor’s expansion is a powerful tool to approximate a function, it is said the Euler, a genius, just by staring at these Taylor expansion
e raised to i*theta has the geometrical meaning as is the circumference of a circle, cited from wiki of below illustration
when theta = pie,