$\displaystyle m*z^2 - D*z +k = 0

$

Need to find the values of z in terms of real and imaginary. m, D and k are all constants. Help would be much aprecciated!

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- Aug 27th 2008, 06:10 AMiphysicsFinding Real and Imaginary
$\displaystyle m*z^2 - D*z +k = 0

$

Need to find the values of z in terms of real and imaginary. m, D and k are all constants. Help would be much aprecciated! - Aug 27th 2008, 06:16 AMMoo
Hello,

Just find the discriminant !

$\displaystyle \Delta=D^2-4km$

The solutions are thus $\displaystyle z=\frac{D \pm \sqrt{D^2-4km}}{2m}$

If $\displaystyle D^2-4km <0$, we can write $\displaystyle D^2-4km=(-1)*\underbrace{(4km-D^2)}_{>0}=i^2 \cdot (4km-D^2)$

$\displaystyle \implies z=\frac{D \pm i ~\sqrt{4km-D^2}}{2m}=\frac{D}{2m} \pm i ~\frac{\sqrt{4km-D^2}}{2m}$

What are the real and imaginary parts ? (Tongueout) - Aug 27th 2008, 06:20 AMiphysics
Thanks for that man. Im going to scan the document in another topic, because it is near impossible for me to do. Will upload ASAP

BTW, The real component is = to $\displaystyle D/2m$. Dont know how to explain the negative sign!? - Aug 27th 2008, 07:46 AMmr fantastic