# Thread: help me in complex numbers

1. ## help me in complex numbers

Using De’Moivre’s Theorem, prove that

cos^4 θ= 1/8 cos4θ + 1/2 cos2θ+ 3/8

Kindly show the solution,

Thanks.

2. Originally Posted by Salman91
Using De’Moivre’s Theorem, prove that

cos^4 θ= 1/8 cos4θ + 1/2 cos2θ+ 3/8

Kindly show the solution,

Thanks.
Show us what you have done, then we will explain any errors

CB

4. Originally Posted by Salman91

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

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

5. Originally Posted by CaptainBlack
$\displaystyle \displaystyle (\cos (\theta)+i \sin(\theta))^4= \cos(4\theta)+i\sin(\theta)$
$\displaystyle (\cos{\theta} + i\sin{\theta})^4 = \cos{(4\theta)} + i\sin{(4\theta)}$.