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November 01, 2025, 07:57:51 pm
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Author Topic: Find K Integer Question (VCAA 2004)  (Read 664 times)  Share 

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Find K Integer Question (VCAA 2004)
« on: October 16, 2009, 11:28:40 pm »
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Has anyone done question 5 from the VCAA 2004 Exam 1?

The question is let w =

a) Express w in exact polar form. (Answer is )
b) Hence find the positive integer k for which

Any help would be greatly appreciated  :)
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mark_alec

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Re: Find K Integer Question (VCAA 2004)
« Reply #1 on: October 16, 2009, 11:43:05 pm »
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de Moivre's theorem states that . That will be equal to 1 when the argument is a multiple of
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kamil9876

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Re: Find K Integer Question (VCAA 2004)
« Reply #2 on: October 16, 2009, 11:44:08 pm »
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However this is an integer if and only if n is a multiple of 5. Hence the values of are all integer multiples of 12. The positive values of are
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."
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