Jim 419 – Complex Variables - Solution to Tutorial 2 Questions

PUSAT PENGAJIAN PENDIDIKAN JARAK JAUH

UNIVERSITI SAINS MALAYSIA

ACADEMIC SESSION 2013/2014

JIM 419 – Complex Variables

Solution to Tutorial 2 Questions

1. Determine [pic 1]

       Let  [pic 2]

            Then  [pic 3]

            let  [pic 4]

             [pic 5]

        [pic 6]

        [pic 7]

        [pic 8]

        [pic 9]

        [pic 10]

1.  Determine [pic 11]

       Let  [pic 12]

            Then  [pic 13]

            let  [pic 14]

             [pic 15]

        [pic 16]

        [pic 17]

        [pic 18]

        [pic 19]

        [pic 20]

1. 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]

1. 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].