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owlet
 one year ago
Question and my solution below.
Which part did I do wrong?
owlet
 one year ago
Question and my solution below. Which part did I do wrong?

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owlet
 one year ago
Best ResponseYou've already chosen the best response.0This is a review question and my book only has the solution & answers to odd number questions and this is an even number question. My answer is not even one of the choices lol

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1I see no error in your working...

owlet
 one year ago
Best ResponseYou've already chosen the best response.0are you sure? maybe the book is wrong. thanks for confirming it :) I'll probably ask my prof about that.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1yup http://www.wolframalpha.com/input/?i=cube+roots+of+%2833i%29

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1you are starting with \[\sqrt[3] { 3e^{\frac {\pi } {4} } } \]??

owlet
 one year ago
Best ResponseYou've already chosen the best response.0why is it 3? r is equal to \(\sqrt{18}\), so I have multiply it by the nth power which is 1/3 so it will be \(\sqrt[6]{18}\) since 1/2 times 1/3 is 1/6. De moivres + euler's formula: \(\large z^n=r^ne^{in \theta}\) sub the values in..it will be: \(\large z^{1/3}=\sqrt[6]{18}e^{i \frac{1}{3}( \frac{5 \pi}{4} + 2 \pi k)}\)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1if we draw it first we have this dw:1442695851885:dw which kinda makes it easy as we have \(3 e^{i \frac{5 \pi}{4}}\)

owlet
 one year ago
Best ResponseYou've already chosen the best response.0ok. I got that.. but where did the "3" came from?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1sorry we have \(\sqrt{18} e^{i \frac{5 \pi}{4}}\) which gives \(\large \sqrt[3]{\sqrt{18} \, e^{i(\frac{5 \pi}{4} + 2n\pi)} }\) \(\large = \sqrt[6]{18} \sqrt[3]{ \, e^{i(\frac{5 \pi}{4} + 2n\pi)} }\) \(\large =\sqrt[6]{18} \ \, e^{i(\frac{5 \pi}{12} + \frac{2n\pi}{3})} \) \(\large = \sqrt[6]{18} \ \, e^{i(\frac{5 \pi + 8n \pi}{12}) } \) \(\large \implies \sqrt[6]{18} \ \, e^{i(\frac{5}{12}) } \) \(\large \implies \sqrt[6]{18} \ \, e^{i(\frac{13}{12}) } \) \(\large \implies \sqrt[6]{18} \ \, e^{i(\frac{21}{12}) } \)

owlet
 one year ago
Best ResponseYou've already chosen the best response.0we got the same! :D the method is the same, I just used exponents instead of radical. Thanks for clarifying it also. I already sent a message to my prof. I'm just waiting for his response.
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