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$(2-i)z + (2+i)\overline{z} = 20.$ Where does this intersect the real axis? Currently, I am thinking of going into the format of az+b$\overline{z}$ but I don't think this will bring me anywhere. Any ideas?

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1 Answer 1

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If $z$ is real, then $z = \overline{z}$ and the equation becomes $$ (2+i)z + (2-i)z = 20, $$ i.e., $$ 4z = 20. $$

Hence the intersection with the real axis is $z = 5$.

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