© 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

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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?