Riemann Surface Lab
Map
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powers and roots
zⁿ
zᵗ
zᵃ
polynomials
any polynomial
az²+bz+c
z³+cz+d
exponential and trig
eẓ
sin z
cos z
tan z
affine and Möbius maps
az+b
(az+b)/(cz+d)
n
−
3
+
m
−
2
+
n
−
3
+
a =
+
i
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◫
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n
−
4
+
Examples
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handout 2.3.A
z³ − 3z
z³ − 3z − 2i
z³ + 3z
z³
quadratic
z² − 1
move roots
p(z)
edit cuts
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z→w
w→z
sheets
surface
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grid
labels
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phase
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exponent a
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rationals
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the constants
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a
b
c
d
a
=
+
i
examples
quadratic
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z-plane · p(z)
w-plane
the polynomial
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