M417
Fall 1996
hw3.tex due September 20, 1996
1.
Verify that
a)
sin(x+iy) = sin(x)cosh(y) + i cos(x)sinh(y) .
b)
|sin(x+iy)| = |sin(x)|
2
+|sinh(y)|
2
.
2.
(Rules and nonrules for logarithms)
a)
Show that the set of values of log(i
1
/
2
) is the same as the set of values of
1
/
2
log(i).
b)
Show that the set of values of log(i
2
) is not the same as the set of values of 2 log(i).
3.
Th number(s) i
i
.
a)
Find all values of i
i
.
b)
Show that all values of i
i
are real.
c)
Show that the set of values of i
i
is unbounded and has a limit point at z = 0.
File translated from T
E
X by
T
T
H
, version 4.06.
On 06 Feb 2017, 13:02.