help me in complex numbers

Jan 2010
15
0
Using De’Moivre’s Theorem, prove that

cos^4 θ= 1/8 cos4θ + 1/2 cos2θ+ 3/8

Kindly show the solution,

Thanks.
 
Jan 2010
15
0
i don't know thats why i have come here, so please help me
 

CaptainBlack

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i don't know thats why i have come here, so please help me
Start with:

\(\displaystyle \displaystyle (\cos (\theta)+i \sin(\theta))^4= \cos(4\theta)+i\sin(4\theta)\)

Expand the left hand side and equate real parts on both sides of the resulting equation. Now it should be just an exercise in the repeated application of trig identities.

CB
 
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Prove It

MHF Helper
Aug 2008
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Start with:

\(\displaystyle \displaystyle (\cos (\theta)+i \sin(\theta))^4= \cos(4\theta)+i\sin(\theta)\)

Expand the left hand side and equate real parts on both sides of the resulting equation. Now it should be just an exercise in the repeated application of trig identities.

CB
Actually it's

\(\displaystyle (\cos{\theta} + i\sin{\theta})^4 = \cos{(4\theta)} + i\sin{(4\theta)}\).
 
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