De Moivre's Theorem

vanalm

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Mar 21, 2006
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7
I'm doing my homework and i keep getting a positive angle, but the answer is saying the angle is negative. why is this negative?

(3-i)^6

r=square root of 10

a=r cos alpha

alpha=3/square root of 10

alpha=18.43494882

I have done this and similar problems over and over and can't figure out how they get alpha= -18.43493882
 

pka

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Jan 29, 2005
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8,426
\(\displaystyle \L
3 - i = \sqrt {10} \left( {\cos (\theta ) + i\sin (\theta )} \right),\;\theta = \arctan \left( {\frac{-1}{{ 3}}} \right)\)
 

galactus

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Sep 28, 2005
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Because you have \(\displaystyle (3-i)\)

Coordinates (3,-1) are in the 4th quadrant.

\(\displaystyle tan^{-1}(\frac{-1}{3})=-18.43494882\)

\(\displaystyle (\sqrt{10})^{6}(-.352-i(.936))=-352-936i\)
 

vanalm

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Mar 21, 2006
Messages
7
thanks guys. i got it now.
 
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