anonymous
  • anonymous
Please help! :) What are the three roots of 27(cos (9π/5) i sin (9π/5))? Express the answers in trigonometric form.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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dumbcow
  • dumbcow
im guessing you mean the 3 solutions of the cube root of given complex number \[\sqrt[3]{r(\cos \theta +i \sin \theta)} = \sqrt[3]{r}(\cos \frac{2\pi k +\theta}{3} +i \sin \frac{2\pi k+\theta}{3})\] where k = 0,1,2
dumbcow
  • dumbcow
so for k=1 \[\frac{2\pi+ \frac{9\pi}{5}}{3} = \frac{\frac{10\pi}{5}+ \frac{9\pi}{5}}{3} = \frac{19\pi}{15}\] \[\rightarrow 3(\cos \frac{19\pi}{15}+ i \sin \frac{19\pi}{15})\] that is 1 root
anonymous
  • anonymous
How do you substitute the next value of k in?

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dumbcow
  • dumbcow
well k=0 is easy ... the "2pi" part goes away for k=2, just replace k with 2 ..... 2*2pi = 4pi
anonymous
  • anonymous
Wait... I got 3π/5 and 29π/15 as the other 2 roots
dumbcow
  • dumbcow
correct
anonymous
  • anonymous
Cool... thanks. I think I understand it now
dumbcow
  • dumbcow
no problem

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