M417
Fall 1996
hwcr.tex due September 14, 1996
1.
Verify that f(z) =
―
z = x − iy is not differentiable at any point z.
2.
Verify that f(z) = |z
2
| is differentiable only at z=0.
3.
The complex exponential function e
z
is defined as
exp(z) = e
z
= e
x
(cos(y) + i sin(y)).
Verify that e
z
satisfies the Cauchy-Riemann equations for all z .
4.
Discuss
lim
z→∞
e
z
.
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, version 4.06.
On 06 Feb 2017, 11:46.