gokturkv Posted October 10, 2014 Report Share Posted October 10, 2014 Hi guys, I am struggling with a question and I couldn't solve it. Can you help me ? z= Reply Link to post Share on other sites More sharing options...
Ossih Posted October 10, 2014 Report Share Posted October 10, 2014 I'm going to assume you know de Moivre's theorem so if z = cos x + i sin x then z = e^ix 1/z^n = z^-n = (z^n)^-1 = (cos (-x) + i sin (-x)) = cos x - i sin x (because cos x is an even function) So, z + 1/z = cos x + i sin x + cos x - i sin x = 2cos x which is real. So Im(z + 1/z) = 0 2 Reply Link to post Share on other sites More sharing options...
Vioh Posted October 10, 2014 Report Share Posted October 10, 2014 Ossih has a perfect answer for 5(a). However it seems that you also ask for help for question 5(b), so I’ll write down the whole worked solution here: Tell me if anything is unclear 2 Reply Link to post Share on other sites More sharing options...
gokturkv Posted October 11, 2014 Author Report Share Posted October 11, 2014 I understood Thank you so much Reply Link to post Share on other sites More sharing options...
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