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tsopatsopa
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Complex analysis and complex plane
- Thread starter tsopatsopa
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SUMMARY
The discussion focuses on the complex function defined by f(z) = u + vi, where u = sin(x) * cosh(y) and v = cos(x) * sinh(y). Participants are tasked with determining the trajectory of the point (u, v) based on the trajectory of the complex number z = x + yi. The suggestion is made to select specific points on the trajectory of z and substitute these values into the function to analyze the resulting path in the (u, v) plane.
PREREQUISITES- Understanding of complex numbers and their representation in the complex plane.
- Familiarity with hyperbolic functions such as sinh and cosh.
- Basic knowledge of trigonometric functions, specifically sine and cosine.
- Ability to perform substitutions in mathematical functions.
- Explore the properties of complex functions and their mappings in the complex plane.
- Study the behavior of hyperbolic functions in relation to trigonometric functions.
- Learn how to visualize complex functions using software tools like MATLAB or Python's Matplotlib.
- Investigate the concept of trajectories in the context of complex analysis.
Students studying complex analysis, mathematicians interested in complex functions, and educators teaching advanced mathematics concepts.
- #2
I like Serena
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Welcome to PF, tsopatsopa! 
Pick a couple of points on the trajectory and plug the numbers into your function?
Pick a couple of points on the trajectory and plug the numbers into your function?
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