Complex numbers (1 Viewer)

kaz1 · Oct 11, 2009

kaz1 · Oct 11, 2009

untouchablecuz · Oct 11, 2009

can anyone suggest a more elegant method for i)?

also, i'm not sure how α is related to β

Trebla · Oct 11, 2009

Alternative method for (i):

$\let $ u=r_1cis\alpha, w=r_2cis\beta\\u\bar{w}+w\bar{u}=0\\\Rightarrow r_1r_2[cis(\alpha)\times cis(-\beta)+cis(-\alpha)\times cis(\beta)]=0\\\Rightarrow [cis(\alpha-\beta)+cis(-(\alpha-\beta))]=0\\$ as $ r_1,r_2\neq 0\\\Rightarrow 2\cos(\alpha-\beta)=0\\\therefore \cos(\alpha-\beta)=0\\$Consider $\\u\bar{w}=\cos(\alpha-\beta)+i\sin(\alpha-\beta)\\Re(u\bar{w})=\cos(\alpha-\beta)\\= 0 $ from above result$

$Re(u\bar{w}) = 0\\$Divide both sides by $ w \bar{w}$ which is always real $\\\\\dfrac{Re(u\bar{w})}{w\bar{w}}= 0\\\\Re\left (\left\dfrac{u\bar{w}}{w\bar{w}} \right)=0\\\\\therefore Re\left (\dfrac{u}{w} \right )=0$

shaon0 · Oct 11, 2009

untouchablecuz said:
can anyone suggest a more elegant method for i)?

also, i'm not sure how α is related to β

I'll give you a clue for relating Alpha and Beta. 2atan(1/2)=tan(4/3). You're file isn't opening on mine.

untouchablecuz · Oct 11, 2009

oh im an idiot

$arg(\frac{u-w}{u+w})=\theta \Rightarrow \theta =tan^{-1}\frac{4}{3}$

untouchablecuz · Oct 11, 2009

shaon0 said:
I'll give you a clue for relating Alpha and Beta. 2atan(1/2)=tan(4/3). You're file isn't opening on mine.

hm ill reupload it

shaon0 · Oct 11, 2009

untouchablecuz said:
hm ill reupload it

Stuff it, it's still not opening. It's probably my internet settings. Good work anyway.

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Complex numbers (1 Viewer)

kaz1

et tu

kaz1

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untouchablecuz

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Trebla

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shaon0

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untouchablecuz

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untouchablecuz

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