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Question
Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`
Solution
z1 = 2 – i, z2 = –2 + i
`((z_1z_2)/barz_1) = ((2 - i)(-2 +i))/(2 -i) = (-(2 - i)(2 -i))/(2 + i)`
= `- (2-i)^2/(2 + i) = (- (4 + i^2 - 4i))/(2 + i)`
= `(-(4 - 1 - 4i))/((2 + i)) = -(3 - 4i)/(2 + i)`
= `-(3 - 4i)/(2 + i) xx (2 - i)/(2 - i)`
= `(- 6 - 4i^2 + 3i + 8i)/(4 - i^2) = (- 6 + 4 + 11i)/(4 + 1)`
= `(- 2 + 11i)/5 = - 2/5 + 11/5 i`
Re`((z_1z_2)/barz_1) = - 2/5`
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