MHB Find Complex Root of z^5=0 | Math Solutions

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The equation z^5 = 0 has one real root, which is 0. Additionally, it has a single complex root, also 0, but with a multiplicity of 5. This means that the root 0 is repeated five times in the context of the equation. The discussion emphasizes the nature of the roots in complex analysis. Understanding these roots is essential for solving polynomial equations in mathematics.
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how to find the complex root of

z^5 = 0 there is one real root 0
 
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This equation has a single complex root, i.e., 0.
 
Evgeny.Makarov said:
This equation has a single complex root, i.e., 0.

with a multiplicity of 5.
 
thanks
 

Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
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