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November 16th, 2017, 03:31 AM   #1
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Proof that real part of complex number is equal 0

Given that $\displaystyle w = 1 + \sqrt{3}$ and $\displaystyle z = 1 + i $ show that $\displaystyle \Re(\frac{\sqrt{2}z + w}{\sqrt{2}z - w}) =
0$

I only found that $\displaystyle \Re(w) = \frac{1}{2}
(w + \bar{w})$ but still I have no idea how to solve it.
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November 16th, 2017, 04:09 AM   #2
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I suspect you should have $w - \bar{w}$ in your simplification. The solution then follows by thinking about the real part of any complex number minus its own conjugate.
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November 16th, 2017, 09:07 AM   #3
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Why use the conjugate? Just fill in w and z in the given expression.
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November 16th, 2017, 11:10 AM   #4
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I suggest, aga150, that you correct the mistake in the statement of the problem.
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