Secret Kinks of Elementary Functions

What happens to graphs between degrees of polynomials? How can we draw complex inputs and outputs in 2 dimensions? And what will we see if we try? 00:00 Intro 01:14 The Messy Powers 04:41 About Complex Numbers 07:15 Importing a Function into the Complex Plane 12:19 Overshooting with Euler 17:27 Roots 23:30 Flower Pressing 25:47 Down to and Around Zero 27:06 The Big Bang 29:34 Enjoy! 30:53 Bonus Functions CORRECTIONS: 03:26 The first x in the expansion is raised to 1.4. It should be raised to 1.6. DESMOS GRAPHS: =============== 5th degree polynomial x^p x^x base Gaussian More on Complex Numbers: Music by: @timkuligfreemusic (intro) @Lisayamusic (the rest of the video) Notes: At 2:46, when we start converting fractional powers, the fractions must be reduced to lowest terms before we use them to assign the degree of root and power under it.