THE UNIVERSITY OF TEXAS AT AUSTIN
Dept. of Electrical and Computer Engineering
EE313 Linear Systems and Signals
HW1
Due: 02/01/2010
Problem 1.1 Properties of Complex Numbers
Given that z
1
= r1e
jθ1
and z
2
= r2 e
jθ2
express the following operations in terms
of r1, θ1, r2, and
θ2 and simplify as much as possible.
(a) z
1
*
(b) z
2
2
(c) z
1
/ z
2
(d) z
1
+z
1
*
e)z1jz1
*
f)z1z1
*
Part II: Double check your simplifications by using z1 = 3 +4j and z2 = 1 + 2j. This
might be a good opportunity to write a Matlab script to compare the original expression
with the simplified expression for each case above. In comparing numeric calculations for
the original “o”and simplifed “s” expressions, you can consider them equal if
i.e
that the relative error is less than 10
10
.
Hint: Be careful when converting a complex number in Cartesian form to polar form.
Getting the right quadrant of the angle is important. In order to compute the angle for a
complex number x+jy, you could use ArcTan[x, y] in Mathematica or atan2(y, x) in Matlab.
When writing a number in polar form, one format is to use Ae
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 Spring '08
 Shafer
 Mathematica, Complex number, Euler's formula

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