# An algebra problem by abhi jith

Algebra Level pending

Let $$z_1$$ and $$z_2$$ be complex numbers satisfying $$z + \bar z = 2|z-1|$$ and $$\arg(z_1 - z_2 ) = \frac \pi4$$.

Which of the following statements are true?

A: $$\ \Re(z_1+z_2)=2$$
B: $$\ \Im(z_1+z_2)=2$$
C: $$\ z_1$$ and $$z_2$$ lies on a parabola.
D: $$\ z_1$$ and $$z_2$$ does not exist.

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