HW7
Tian Gu
Code: 815
10/17/2010
Problem 1
This is a complex number problem
A=3+2j B= 5e
jp/3
C= 3 with and angle of 30
0
a)
Find A*B in rectangular and exponential forms
b)
Find A/C in rectangular and exponential forms
c)
Find (A*C)/B in rectangular and exponential forms
Problem 2
Introduction: Vector is a tool in mathematics and physics. And it is also a class template in programming
like C++.
cross product
: In physics, sometimes the notation a
∧
b is used.
The definition of the cross product can also be represented by the determinant of a formal matrix:
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We can use Sarrus' rule and Cofactor expansion.
Sarrus' Rule
Cofactor expansion
Problem 3
Write the following exponentials in real and imaginary forms
j5e
2j
, j2e
j
p
/4
, Ae
j
p
, j6e
j
p
/2
Problem 4
Read the following
article about lasers
and answer the following questions
a)
What is a size of semiconductor lasers
The kinds of lasers used in optical networks are tiny devices — usually about the size of a grain of salt.
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 Fall '09
 Light, Stimulated emission, Semiconductor LASERs, exponential forms

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