MAT067
University of California, Davis
Winter 2007
Homework Set 1: Exercises on Complex Numbers
Directions
: You are assigned the
Calculational Problems
1(a, b, c), 2(b), 3(a, b), 4(b,
c), 5(a, b), and the
ProofWriting Problems
8 and 11.
Please submit your solutions to the Calculational and ProofWriting Problems
separately
at the beginning of lecture on Friday January 12, 2007. The two sets will be graded by
di±erent persons.
1. Express the following complex numbers in the form
x
+
yi
for
x, y
∈
R
:
(a) (2 + 3
i
) + (4 +
i
)
(b) (2 + 3
i
)
2
(4 +
i
)
(c)
2 + 3
i
4 +
i
(d)
1
i
+
3
1 +
i
(e) (
−
i
)

1
2. Compute the real and imaginary parts of the following expressions, where
z
is the
complex number
x
+
yi
and
x, y
∈
R
:
(a)
1
z
2
(b)
1
3
z
+ 2
(c)
z
+ 1
2
z
−
5
(d)
z
3
3. Solve the following equations for
z
a complex number:
(a)
z
5
−
2 = 0
(b)
z
4
+
i
= 0
(c)
z
6
+ 8 = 0
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(d)
z
3
−
4
i
= 0
4. Calculate the
(a) complex conjugate of the fraction (3 + 8
i
)
4
/
(1 +
i
)
10
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 Fall '07
 Schilling
 Linear Algebra, Algebra, Complex Numbers, Complex number, C. Prove

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