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Complex Variable Test II
For complex variables
15
Mathematics
Graduate
03/18/2020
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Term
sin(z)
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cos(z)
 Definition
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sinh(z)
 Definition
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cosh(z)
 Definition
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Term
zα
 Definition
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cos(z)
 Definition
cosh(iz)
Term
cosh(z)
 Definition
cos(iz)
Term
i sin(z)
 Definition
sinh(iz)
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i sinh(z)
 Definition
sin(z)
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ez
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exeiy = ex(cos(y) + i sin(y))
Term

z = reiθ

what is r?

what is θ?

 Definition

r = |z|

θ = arg(z) = arctan(z)
Term
e-iθ
 Definition
cos(θ) - i sin(θ)
Term
eiθ
 Definition
cos(θ) + i sin(θ)
Term
log(z)
 Definition
Log(z) + 2πim = log|z| + i arg(z) + 2πim
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Cauchy Integral Formula

F(m)(z) = 

 Definition
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