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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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