owlet
  • owlet
Question and my solution below. Which part did I do wrong?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
owlet
  • owlet
owlet
  • owlet
This 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
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hartnn
  • hartnn
I see no error in your working...

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owlet
  • owlet
are you sure? maybe the book is wrong. thanks for confirming it :) I'll probably ask my prof about that.
hartnn
  • hartnn
yup http://www.wolframalpha.com/input/?i=cube+roots+of+%28-3-3i%29
IrishBoy123
  • IrishBoy123
you are starting with \[\sqrt[3] { -3e^{\frac {\pi } {4} } } \]??
owlet
  • owlet
why 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
  • IrishBoy123
if 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
  • owlet
ok. I got that.. but where did the "3" came from?
IrishBoy123
  • IrishBoy123
sorry 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
  • owlet
we 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.
IrishBoy123
  • IrishBoy123
good luck!

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