homework4 (2)

# homework4 (2) - 2 log i z i-z 5 BC p 115 problem 6 Derive...

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Due 02-06-09 Physics 132 Winter 2009 P. Kraus HOMEWORK #4 Hand into box marked “132” outside 1-707D PAB by 3pm Fri. —————————————————————————————————————————— 1) BC p. 97 problem 5: Show that a) the set of values of log( i 1 / 2 ) is ( n + 1 4 ) πi ( n = 0 , ± 1 , ± 2 ,... ) and the same is true of (1 / 2)log i . b) the set of values of log( i 2 ) is not the same as the set of values of 2log i . 2) BC p. 104 problem 1: Show that a ) (1 + i ) i = e - π 4 +2 e i ln 2 2 ( n = 0 , ± 1 , ± 2 ,... ) b ) ( - 1) 1 = e (2 n +1) i ( n = 0 , ± 1 , ± 2 ,... ) 3) BC p. 104 problem 9: Assuming that f 0 ( z ) exists, state the formula for the derivative of c f ( z ) . 4) BC p. 115 problem 5: Derive the expression tan - 1 z = i
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Unformatted text preview: 2 log i + z i-z 5) BC p. 115 problem 6: Derive the expression d dz tan-1 z = 1 1 + z 2 6) BC p. 121 problem 2: Evaluate the following integrals a ) Z 2 1 ( 1 t-i ) 2 dt , b ) Z π/ 6 e i 2 t dt c ) Z ∞ e-zt dt (Re z > 0) 7) BC p. 121 problem 3: Show that if m and n are integers, Z 2 π e imθ e-inθ dθ = ‰ 0 when m 6 = n 2 π when m = n 8) Give parametric expressions z ( t ) for the following two contours a) A straight line connecting z = 3-i and z = 5 + 4 i . b) A circle of radius 2 centered at the point z =-1 + i . Remember to give the range of t in each case. 1...
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