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Post by Admin on Dec 5, 2016 16:18:44 GMT
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Gary
GaryVasco
Posts: 3,352 
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Post by Gary on Dec 13, 2016 22:52:50 GMT
Vasco, This is mine. I think the reasoning is essentially the same. I forgot there was a part (ii), so I'll replace this when I finish it (replaced with (i)-(v), Dec 14). nh.ch6.ex13.pdf (460.15 KB) Gary |
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Post by Admin on Dec 14, 2016 7:57:20 GMT
Gary
There are 5 parts all together.
Also (I don't have access to the book) I think we are only concerned with origin-centred circles and rays through the origin in the KD in part (i), as the exercise mentions $r=const.$ (origin-centred circles). and $\theta=const.$ (lines through the origin).
Vasco
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Dec 14, 2016 16:27:50 GMT
Vasco,
Regarding those circles: I don't understand why r = const. or $\theta$ = const. would place any constraint on the coordinates of the center of the circles. But if I am wrong, then my answer is doubtless also wrong, so it should contain an obvious error. Oh, I see now that the constraint is introduced by the first sentence of the problem where we are to consider $z = re^{i\theta}$. I forgot to reread that when I did part (i). Still, I'm not certain my answer is wrong if one relaxes the constraint on the centers of the circles, but it is easier to see with concentric circles centred at the origin. I have corrected my answer and introduced this issue.
Gary
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