Fundamentals of Engineering Analysis EGR 1302 - Time based and expanded Complex Numbers
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Transcript of Fundamentals of Engineering Analysis EGR 1302 - Time based and expanded Complex Numbers
© 2005 Baylor UniversitySlide 1
Fundamentals of Engineering AnalysisEGR 1302 - Time based and expanded Complex Numbers
© 2005 Baylor UniversitySlide 2
)( qipcez
Expanding the Exponential Form
qcez p cos)Re(
qcez p sin)Im( pcezz mod
qz arg
qip ecez *
)sin(cos qiqcez p
Polar Form
Standard Form
qceiqcez pp sin*cos
© 2005 Baylor UniversitySlide 3
)23(6 iez
Numerical Example with the TI-89
iz 6.1092.50
ieez 23 *6
5.1206 3 ez
2
2.50)2cos(*5.120
)2sin2(cos5.120 iz
© 2005 Baylor UniversitySlide 4
Finding Complex Roots on the TI-89
iz 445 0445 izor
201157.0
© 2005 Baylor UniversitySlide 5
ierz 111
Complex Numbers as a Function of Time
ierz 222
ierrzz )(2121
21*
ticetz )()(
tetx t 15cos01.0)( 02.0
0 5 1010
0
108.847
6.88
g x( )
100 x
0.01Exponential Decay
titecetz )()(
tcetz )(
t
)sin(cos)( tite ti titeetz )15(02.001.0)(
tietz )1502.0(01.0)(
)](Re[)( tztx
)15sin15(cos01.0)( 02.0 titetz t
© 2005 Baylor UniversitySlide 6
Finding Complex Roots
iz 445
You will be expected to use the TI-89 to find Roots.
5)24
(*2444 zei
in
4
24
4
-4
5/1)24
(5/15/15 ][*)24()(in
ezz
inez
*)20
1
20
8(
*2
4,3,2,1,0n
Roots
201,0 n
207,1 n
2
208
201
2039,5 n
© 2005 Baylor UniversitySlide 7
Practical Exercise with Complex Number Formats
ii eiez 5.0)2.12( )32(5.2
)Re(z
)Im(z)mod(z
)arg(z
)(zconj
42 24 izz
1. For
Find:z in Standard Form:
z in Polar Form:
z in Exponential Form:
Plot z on the Argand Diagram
2. Find all the Roots of
© 2005 Baylor UniversitySlide 8
Questions?