sswann222
  • sswann222
an important corollary to the euler identity i DeMoivre's Theorem, which finds the powers and roots of any complex number. let z=x + iy be a complex number, which we associate with point (x,y) in the plane. using polar coordinates we write z = r(cos theta + i sin theta) = re^i (theta), so that z^m = r e^ (i m theta) = r^m (cos m theta + i sin m theta) (i) z = 1 + i and m = 10 then, (ii) find all six of the roots to x^6 - 1 = 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[z= r\cos\theta + r\sin\theta i = 1 +i\\ r\cos\theta=1\\ r\sin\theta=1\\ r=?\\ \theta=? \] Can you solve this part to find z polar coordinates?
sswann222
  • sswann222
|dw:1370278151466:dw| we have tried and don't seem to be able to get very far. This is the figure that goes along with it.
sswann222
  • sswann222
i also know that DeMoivre's therem \[(\cos 10\theta + i \sin 10\theta) can be written as (\cos \theta + i \sin \theta) ^ 10\]

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