generated from smyalygames/quartz
9 lines
414 B
Markdown
9 lines
414 B
Markdown
# Definition
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A [[Complex Functions|complex function]] $f(z)$ can be seen as a function of two real variables. Hence
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$$f(z) = f(x + iy) = f(x, y).$$
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When interpreted appropriately.
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> [!example] For instance
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> $$f(z) = z^2 = (x + iy)^2 = x^2 - y^2 + 2ixy$$
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Suppose $f$ is [[Differentiable|differentiable]], we should expect **relations** between $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$. |