My Math Forum Proof that real part of complex number is equal 0

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 November 16th, 2017, 03:31 AM #1 Newbie   Joined: Nov 2017 From: Poland Posts: 1 Thanks: 0 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.
 November 16th, 2017, 04:09 AM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 223 Thanks: 120 Math Focus: Dynamical systems, analytic function theory, numerics 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.
 November 16th, 2017, 09:07 AM #3 Senior Member   Joined: Dec 2015 From: holland Posts: 157 Thanks: 37 Math Focus: tetration Why use the conjugate? Just fill in w and z in the given expression.
 November 16th, 2017, 11:10 AM #4 Global Moderator   Joined: Dec 2006 Posts: 18,241 Thanks: 1438 I suggest, aga150, that you correct the mistake in the statement of the problem.

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