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Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Medium2 minPYQ_2002

MathematicsMediumsingle choice

$z$ and $w$ are two non zero complex no.s such that $∣ z ∣ = ∣ w ∣$ and $Arg z + Arg w = π$ then $z$ equals

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Answer:

Solution:

Let $∣ z ∣ = ∣ ω ∣ = r ∴ z = re^{i θ}, ω = re^{i ϕ}$ where $θ + ϕ = π ∴ \overset{ω}{ˉ} = re^{- i ϕ}$ $∴ z = re^{i (π - ϕ)} = re^{i π} \cdot e^{- i ϕ} = - re^{- i ϕ} = - \overset{ω}{ˉ}$

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: PYQ_2002

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