A Spesh question from me

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Neobeo

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Re: A Spesh question from me

« Reply #15 on: February 06, 2008, 12:58:46 pm »

Quote from: Ahmad on February 04, 2008, 11:17:05 pm

Another way. Since $w \ne 0$ ,
Let $z = r\cdot cis(\theta)$ . (r >= 0)
Then, $\frac{1}{w} = (r + \frac{1}{r})\cos \theta + i(r - \frac{1}{r}) \sin \theta$ .
Setting imaginary part equal to zero, since $\frac{1}{w}$ is real, gives $r = \frac{1}{r} \implies r = 1$

I like Ahmad's method. It should also be noted that $sin \theta \neq 0$ since $y=r sin \theta \neq 0$ .

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Neobeo

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