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anonymous
 one year ago
Use DeMoivre's Theorem to find the indicated power of the following complex number.
(3 + 3i)⁴
My work
r = √18 and tan θ = 1 so θ = 135° because the complex number is in Quadrant II.
√18 [cos(135°) + i sin(135°)]
(√18)⁴ [cos(4 × 135°) + i sin(4 × 135°)]
324[cos(540°) + i sin(540°)]
324(1 + i × 0)
324(1)
324
anonymous
 one year ago
Use DeMoivre's Theorem to find the indicated power of the following complex number. (3 + 3i)⁴ My work r = √18 and tan θ = 1 so θ = 135° because the complex number is in Quadrant II. √18 [cos(135°) + i sin(135°)] (√18)⁴ [cos(4 × 135°) + i sin(4 × 135°)] 324[cos(540°) + i sin(540°)] 324(1 + i × 0) 324(1) 324

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just need to know if I am correct

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hmm I took a very different approach, got the same result though. Yay good job, looks correct! :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1https://www.wolframalpha.com/input/?i=%283%2B3i%29%5E4 Just in case you need to verify ^

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If you dont mind, can you show me how you did it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0either way thanks a lot :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1My method is a little strange. I factor a 3 out to start.\[\large\rm 3^4(1+i)^4\]I recognize that the magnitude of the real and imaginary parts are the same, that only happens at the pi/4 angles. So we need to turn these into sqrt(2)/2's. So I'll factor a sqrt(2) out of each term.\[\large\rm 3^4(\sqrt{2})^4\left(\frac{\sqrt2}{2}+\frac{\sqrt2}{2}i\right)^4\]And as you said, this is in quadrant 2, so it's 3pi/4.\[\large\rm 3^4(\sqrt{2})^4\left(\cos\frac{3\pi}{4}+i \sin\frac{3\pi}{4}\right)^4\]Then, De'Moivre gives us,\[\large\rm 3^4(\sqrt{2})^4\left(\cos3\pi+i \sin3\pi\right)\]Sine is 0 at the 3pi angle, cosine 1,\[\large\rm 3^4(\sqrt{2})^4\left(1+0\right)\]And then just simplify a little further to get the same result. I know, I know, my method is a little goofy :) But I like it lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hahaha thanks a lot man, whatever gets the job done :P
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