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CalcExplorer

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Okay, so I'm working with a rather frustrating problem with a calculus equation. I'm trying to solve a calculus equation which I conceptualized from existing methods involving complex number fractal equations. I'm very familiar with pre-calculus, while being self-taught in portions of calculus for practical applications in coding and higher dimensional mathematics, so bare with me on this.

Here's the premise:

I'm using the Mandelbrot Equation [ z = z

This

z = z

I'm attempting to solve the first iteration of this new equation in quadratic form, the format the mandelbrot is solved in [ z

From what I've surmised thus far in order to solve such an equation I need to first convert the complex logarithm into a complex exponential using Euler's Formula, and then solve the new formula algebraically to derive the first iterational solution.

There seems to be a basis for this method, albeit with certain conditions in the solutions, and similar questions put up on this forum before, but I don't quite understand the principles enough to solve it myself.

These are the relevant mathematical references on the topic I've been able to find -

http://math.gmu.edu/~rsachs/m114/eulerformula.pdf

https://www.physicsforums.com/threads/eulers-formula-and-complex-logarithms-relationship.559665/

https://www.reddit.com/r/askscience/comments/2e3jnv/logarithms_of_complex_numbers_logarithms_with/

But that's pretty much it and I don't quite grasp how it's converted, since there's no direct examples of this process that I could find with conversions using Euler's Formula and Complex Logarithms.

Is this the proper way to go about solving such a problem?

And is there someone here that can help to find the solution?

Here's the premise:

I'm using the Mandelbrot Equation [ z = z

^{2}+ i C ] and the Hausdorff Dimension [ N = s^{d}], where d = ln(N)/ln(s), to create a new iterational equation, which fractally conforms to an already defined Hausdorff Dimension [ log(20)/log(2+φ) ], where φ = ((√5)+1)/2._{This specific Hausdorff Dimension is of a Dodecahedron Fractal Flake.}This

**provides the new equation:**z = z

^{log(20)/log(2+φ)}+ i CI'm attempting to solve the first iteration of this new equation in quadratic form, the format the mandelbrot is solved in [ z

_{2}= a^{2}-b^{2}+ 2abi ], as it's the format most advantageous for the graphical mapping of the fractal structure.From what I've surmised thus far in order to solve such an equation I need to first convert the complex logarithm into a complex exponential using Euler's Formula, and then solve the new formula algebraically to derive the first iterational solution.

There seems to be a basis for this method, albeit with certain conditions in the solutions, and similar questions put up on this forum before, but I don't quite understand the principles enough to solve it myself.

These are the relevant mathematical references on the topic I've been able to find -

http://math.gmu.edu/~rsachs/m114/eulerformula.pdf

https://www.physicsforums.com/threads/eulers-formula-and-complex-logarithms-relationship.559665/

https://www.reddit.com/r/askscience/comments/2e3jnv/logarithms_of_complex_numbers_logarithms_with/

But that's pretty much it and I don't quite grasp how it's converted, since there's no direct examples of this process that I could find with conversions using Euler's Formula and Complex Logarithms.

Is this the proper way to go about solving such a problem?

And is there someone here that can help to find the solution?

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