1
Home Work 1.
Two pages.
Reading assignments don’t have to be turned in. You can choose to do the problems
in this homework
or
the exercises in sections 2.1–2.5 of my notes posted on the class
website.
1.
Reading assignment.
Read chapter 2 of the notes posted on the class website.
2. Find a way to represent complex numbers as 2
×
2
real
matrices, such that
arithmetic operations (+,
−
,
×
, and
÷
) on complex numbers becomes equivalent
to arithmetic operations on their matrix representations instead. That is, if
T
(
z
)
is the 2
×
2 real matrix representing the complex number
z
, then
T
(
z
1
+
z
2
) =
T
(
z
1
) +
T
(
z
2
)
,
T
(
z
1
−
z
2
) =
T
(
z
1
)
−
T
(
z
2
)
,
T
(
z
1
z
2
) =
T
(
z
1
)
T
(
z
2
)
,
T
(
z
1
/z
2
) = (
T
(
z
2
))
−
1
T
(
z
1
)
,
for all complex numbers
z
1
and
z
2
.
Hint:
The entries of
T
(
z
) will depend on
the real and imaginary parts of
z
. Look at the expression for the product of two
complex numbers and two 2
×
2 matrices.
3. A. Show that the
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 Fall '10
 Chandrashekharan
 Complex Numbers, Complex number, eij

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