Complex NumbersHard
Question
Let z and w be two non-zero complex number such that |z| = |w| and arg (z) + arg π, then z equals
Options
A.w
B.- w
C.
D.
Solution
Since, |z| = |w | and arg (z) = π - arg(w)
Let w = reiθ, then
= re- iθ
∴ z = rei(π-θ) = reiπ . re-iθ
= - re-iθ = -
Let w = reiθ, then
= re- iθ ∴ z = rei(π-θ) = reiπ . re-iθ
= - re-iθ = -
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