Jim 419 – Complex Variables - Solution to Tutorial 2 Questions
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PUSAT PENGAJIAN PENDIDIKAN JARAK JAUH
UNIVERSITI SAINS MALAYSIA
ACADEMIC SESSION 2013/2014
JIM 419 – Complex Variables
Solution to Tutorial 2 Questions
- Determine [pic 1]
Let [pic 2]
Then [pic 3]
let [pic 4]
[pic 5]
[pic 6]
[pic 7]
[pic 8]
[pic 9]
[pic 10]
- Determine [pic 11]
Let [pic 12]
Then [pic 13]
let [pic 14]
[pic 15]
[pic 16]
[pic 17]
[pic 18]
[pic 19]
[pic 20]
- Use the polar form to show that [pic 21]
Let [pic 22]
Let [pic 23]
[pic 24]
then [pic 25]
therefore [pic 26]
Let [pic 27] , [pic 28]
Then [pic 29]
Let [pic 30]
then [pic 31]
therefore [pic 32]
Hence [pic 33][pic 34]
[pic 35]
[pic 36]
[pic 37]
[pic 38]
Therefore [pic 39]
- Find the principal argument Arg z when [pic 40]
[pic 41]
[pic 42]
arg z =11[pic 43]
Therefore the principal argument Arg z = [pic 44].
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