Real Eq's from Complex and visa-versa

KwolZ, 17/07/2021

Closed form, graphical solutions to "elementary" complex functions utilizing two (or more) sets of equations: [f,g](x),-[f,g](x),[f,g](-x),-[f,g](-x): and equations derived from real objects, but utilizing the same partial differential "thing" that makes the other graphs work for some reason. Very little makes sense to me, but I think these look really cool and can be fun to solve, even if I don't know why I did certain things (or why those things worked). So the equations that I find that actually work, or at least seem to do what I was aiming for in some way, are now going to go in this book. So are random things I decide to do with complex numbers. Those will (probably) have separate explanations for each, that way some amount of reason can come from my shenanigans.


  • 1. Complex Integration - The Easy Way
  • 2. x^n planes
  • 3. Any Complex logarithm of any first degree complex Number
  • 4. Complex log of ANY complex root (n must be real)
  • 5. Surface and real Equations for arbitrary complex square root
  • 6. Real equations for the Complex Cubic Root
  • 7. The second and third degree graph of a 1 degree comp. number
  • 8. The complex 4th root. Positive reals only (a>0)
  • 9. All eq graphs for complex fourth, a>1, b<270deg
  • 10. Real eq's for a complex inverse. "lungs and circles"
  • 11. Real EQs for Complex Inverse Square Root
  • 12. Complex inverse cube root
  • 13. Real Equations for the complex... squared cube root? Sure.
  • 14. Real equations for z+z^(1/2)
  • 15. Magical Egg
  • 16. Geometric Eggs, crafted from a cone and a "complex" circle
  • 17. Erf from a complex plane (sorta)- no integration required
  • 18. Complex Equations for sin,cos, and tan
  • 19. An elliptical equation derived from circles

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Complex Integration - The Easy Way

– KwolZ

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