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Date: Wed, 22 Jan 2025 19:04:56 -0800
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On 1/22/2025 3:58 PM, sobriquet wrote:
> Op 22/01/2025 om 14:48 schreef Richard Hachel:
>> x²+4x+5=0
>>
>> This equation has no root, and it never will.
>>
>> We can then find two roots of its mirror curve.
>>
>> Let x'=-3 and x"=-1
>>
>> These are not roots of this curve, but the roots of the imaginary 
>> mirror curve.
>>
>> What is this imaginary mirror curve?
>>
>> It is the curve with equation y=-x²-4x-3
>>
>> Let's look for its roots, and we find x'=-3 and x'=-1
>>
>> These are the imaginary roots of x²-4x+5.
>>
>> Or x'=-3(i) and x'=-1(i)
>>
>> R.H.
> 
> 
> Wolfram Alpha tells us there are two roots:
> 
> https://www.wolframalpha.com/input?i=solve+x%5E2%2B4x%2B5%3D0
> 
> Here you can see the roots:
> 
> https://www.desmos.com/3d/mpwj5h2ab8

The roots are fun to work with in a Julia fractal. They can plot many 
things. An example, my multi julia:

https://paulbourke.org/fractals/multijulia