The discussion centers on solving the equation z + (conjugate of z)^2 = 4, where z is defined as x + iy. The participants clarify the expansion of (conjugate of z)^2, leading to the expression x + x^2 - y^2. They derive that the imaginary part must equal zero, resulting in the conditions y = 0 or x = 1/2, alongside the equation x + x^2 - y^2 = 4. This analysis highlights the importance of correctly handling complex conjugates in algebraic expressions.
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They aren't showing all their steps.gtg177i said:Homework Statement
z+(conjugate of z)^2=4
Homework Equations
z = x+iy
(x+iy)+(x-iy)^2=4
The Attempt at a Solution
the solutions give (x+iy)+(x-iy)^2= x + x^2 - y^2. how do they reach that?
gtg177i said:I get (x+iy)+(x-iy)^2 = x + iy + x^2 -2xiy + i^2*y^2.
I think the question is the ( conjugate of z )^2. e.g. z with the line on top of it and that squared.
Thanks!