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Question
Let z1 and z2 be two complex numbers such that `barz_1 + ibarz_2` = 0 and arg(z1 z2) = π. Then find arg (z1).
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Solution
Given that `barz_1 + ibarz_2` = 0
⇒ z1 = iz2
i.e., z2 = –iz1
Thus arg (z1 z2) = argz1 + arg(–iz1) = π
⇒ arg`(-iz_1^2)` = π
⇒ arg(–i) + arg`(z_1^2)` = π
⇒ arg(–i) + 2arg (z1) = π
⇒ `(-pi)/2 + 2` arg(z1) = π
⇒ arg(z1) = `(3pi)/4`
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