Complex numbers: Prove Re(z) = (1/2)(z + z-with-bar-on-top)

firechicken188

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Hi, first off I'm not sure if this is the appropriate section to post in, but I have a doubt regarding complex numbers:confused::confused::

(a) Prove that, for any complex number \(\displaystyle z\, \in\, \mathbb{C},\) we have:

. . . . .\(\displaystyle \mathcal{Re}(z)\, =\, \dfrac{1}{2}\left(z\, +\, \bar{z}\right)\)
 

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Hi, first off I'm not sure if this is the appropriate section to post in, but I have a doubt regarding complex numbers:confused::confused::

(a) Prove that, for any complex number \(\displaystyle z\, \in\, \mathbb{C},\) we have:

. . . . .\(\displaystyle \mathcal{Re}(z)\, =\, \dfrac{1}{2}\left(z\, +\, \bar{z}\right)\)
If a complex number z is expressed as z = x + iy (where x and y are real functions), then:

1) Re (z) = ??
2) How would you express complex conjugate of z (as a function of x and y)?
 
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