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.
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