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Conformal Mappings
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Flashcards
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f(z) = z^2
Conformal except at z = 0.
f(z) = \frac{1}{z}
Conformal everywhere except at z = 0.
f(z) = \cos(z)
Conformal everywhere in the complex plane.
f(z) = \log(z)
Conformal in the cut plane, excluding z = 0.
f(z) = z \cdot e^z
Conformal everywhere in the complex plane.
f(z) = \tan(z)
Conformal where it is defined (not at points where cos(z) = 0).
f(z) = z^3
Conformal except at z = 0.
f(z) = \frac{1}{z^2}
Conformal everywhere except at z = 0.
f(z) = e^{iz}
Conformal at all points in the complex plane.
f(z) = e^z
Conformal at all points in the complex plane.
f(z) = z + \overline{z}
Not conformal at any point.
f(z) = \sqrt{z}
Conformal in the cut plane, excluding z = 0.
f(z) = \frac{z}{(1+z^2)}
Conformal except where z^2 = -1.
f(z) = \sinh(z)
Conformal everywhere in the complex plane.
f(z) = \arg(z)
Not conformal at any point.
f(z) = \text{Re}(z)
Not conformal at any point.
f(z) = z + \frac{1}{z}
Conformal everywhere except at z = 0.
f(z) = \sin(z)
Conformal everywhere in the complex plane.
f(z) = 1 + z^4
Conformal everywhere in the complex plane.
f(z) = \text{Im}(z)
Not conformal at any point.
f(z) = \overline{z}
Not conformal at any point.
f(z) = \cosh(z)
Conformal everywhere in the complex plane.
f(z) = \cot(z)
Conformal where it is defined (not at points where sin(z) = 0).
f(z) = \frac{1}{1 - z}
Conformal everywhere except at z = 1.
f(z) = \text{sgn}(\text{Im}(z))
Not conformal at any point.
f(z) = \text{sgn}(\text{Re}(z))
Not conformal at any point.
f(z) = z^2 - z
Conformal everywhere except at z = 0 and z = 1.
f(z) = |z|
Not conformal at any point.
f(z) = e^{z^2}
Conformal at all points in the complex plane except at z = 0.
f(z) = \text{sgn}(z - z_0) for some z_0 \in \mathbb{C}
Not conformal at any point.
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