Question

please help me answer all parts of the question in the photo.

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Answer 1

$z_1=4+2i\\z_2=-1+2i\\\overline(z_2)=\sqrt{(-1)^2+(2i)^2}=\sqrt{1-4}=i\sqrt{3}\\ z_1+\overline(z_1)=4+2i+\sqrt{4^2+(2i)^2}=4+2i+\sqrt{16-4}=4+\sqrt{12}+2i\\z_2+\overline(z_2)=-1+2i+\sqrt{(-1)^2+(2i)^2}=-1+2i+\sqrt{1-4}=-1+(2+\sqrt{3})i$