ENEE 241 02*
HOMEWORK ASSIGNMENT 2
Due Tue 02/10
Please turn in the two problems separately, with your name and section number on each sheet (or
set of sheets).
Problem 2A
Do not use a calculator for this problem. Express your answers using square roots and/or fractional
multiples of
π
.
Throughout this problem, let
u
=

√
3 +
j
and
v
=

1

j
(i) (2 pts.)
Express each number in the form
re
jθ
. Plot both numbers on the complex plane.
(ii) (4 pts.)
Let
a
be real. Determine, in terms of
a
, the real and imaginary parts of the complex
number
w
=
a
+
j
u
+
v
For what value(s) of
a
is
w
purely imaginary?
(iii) (5 pts.)
Determine the roots of the equation
z
6

v
2
= 0
and plot them on the complex plane. Are there any conjugate pairs among the roots?
(iv) (3 pts.)
Sketch the circle described by the equation

z

u

= 1
Determine the points of intersection (if any) of this circle and the two axes, real and imaginary.
(v) (3 pts.)
Sketch the line described by the equation

z

v

=

z

Where does this line intersect the two axes? What is the value of its slope?
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 Spring '08
 staff
 Complex number, 3 pts, 5 pts, 2 pts, 4 pts

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