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# HW5 - Physics2210.Homeworkassignment5 B 2.4.4 3 i y(x y = 3...

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1 Physics 2210. Homework assignment 5. B 2.4.4 3 + i (x,y) = ( 3 , 1) 3 +i (r, θ ) = (2, 5 6 π ) 2(cos 5 6 π + i sin 5 6 π ) 2e i 5 6 π The complex conjugate of 3 + i is 3 i . B 2.5.44 x + iy = (1 i) 2 . (1 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 = e i π 4 = e i( π + 2k π ) 4 = e i( π 4 + 2k π 4 ) for k=0,1,2,… The four distinct roots correspond to k=0,1,2,and 3: e i π 4 , e i 3 π 4 , e i 5 π 4 and e i 7 π 4 . Or 1 2 + i 2 , - 1 2 + i 2 , - 1 2 - i 2 , and 1 2 - i 2 . B 2.10.20 8i 3 = 8e i 3 π 2 3 = 2 e i( 3 π 2 + 2k π ) 3 = 2e i( π 2 + 2k π 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

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HW5 - Physics2210.Homeworkassignment5 B 2.4.4 3 i y(x y = 3...

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