HW5 - Physics2210.Homeworkassignment5. B 2.4.4 3+i y (x, y)...

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1 Physics 2210. Homework assignment 5. B 2.4.4 + i (x,y) = ( , 1) 3 +i (r, θ ) = (2, 5 6 π ) 2(cos 5 6 + i sin 5 6 ) 2e i 5 6 The complex conjugate of 3 + i is 3 i . B 2.5.44 x + iy = (1 i) 2 . i) 2 = 2i , and x + iy = 2i . Therefore, x=0 and y=-2. B 2.5.46 x + iy x iy = i . For x and y that are non-zero, we have: (x + iy) = -i(x iy) , or x + iy = -y - ix . Therefore y=-x is the solution, provided that they are non-zero. B 2.10.14. 1 4 = i 4 = i( + 2k ) 4 = e i( 4 + 2k 4 ) for k=0,1,2,… The four distinct roots correspond to k=0,1,2,and 3: e i 4 , e i 3 4 i 5 4 and e i 7 4 . Or 1 + i , - 1 + i 2 1 - i , and 1 - i . B 2.10.20 8i 3 = 8e i 3 2 3 = 2 i( 3 2 + 2k ) 3 = 2e i( 2 + 2k 3 ) for k=0,1,2,… The three distinct roots correspond to k=0,1, and 2: x y A r=2 θ =5/6 π x y r=1 x y r=2
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2 2e i π 2 , 2e i 7 6 , and 2e i 11 6
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This note was uploaded on 11/10/2009 for the course PHYS 2210 at Colorado.

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HW5 - Physics2210.Homeworkassignment5. B 2.4.4 3+i y (x, y)...

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