How Do You Graph the Complex Function w = z^(i+2)?

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SUMMARY

The discussion focuses on graphing the complex function w = z^(i+2), where z is defined as z={z|0<=arg z<=(pi)/6}. Participants suggest visualizing the function through two three-dimensional graphs representing the real and imaginary components. Additionally, they recommend breaking down the mapping into simpler segments to build a clearer visual intuition. The mathematical expression z^k = e^(k log z) is highlighted as a fundamental concept for understanding the transformation.

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alazhumizhu
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For example :
z={z|0<=arg z<=(pi)/6}
Draw w=z^(i+2).
I can draw w=z^2 and w=z^i
But w=z^(I+2)is a holy garbagety
 
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Hey alazhumizhu and welcome to the forums.

You might want to consider drawing two three dimensional graphs (one for the real and one for the imaginary), or look at drawing individual "line segments" of the mapping and building up the visual intuition that way.
 
[tex]z^k=e^{k\log z}[/tex]

Then you can find the image by composing these easier maps.
 

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