Let z and - are two non-zero complex numbers such that - z - - - and z - - - - - then z equal to

The correct option is B ω [ From the help of given question; z=| z | ( cos #160; θ +isin #160; θ ...

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Byju's Answer

Standard XII

Mathematics

Properties of Argument

Let z and ...

Question

Let $z$ and $ω$ are two non-zero complex numbers such that $| z | = | ω |$ and $arg z + arg ω = π,$ then $z$ equal to

ω

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- ω

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¯ ¯ ¯ ω

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- ¯ ¯ ¯ ω

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Solution

The correct option is B $- ¯ ¯ ¯ ω$
$\begin{matrix} F r o m t h e h e l p o f g i v e n q u e s t i o n z = | z | (cos θ + i sin θ) w h e r e θ = z I f θ_{1} = w t h e n tan θ = π - θ_{1} S o, z = | w | (cos (π - θ_{1}) + i sin (π - θ_{1})) = | w | (- cos θ_{1} + i sin θ_{1}) = - | w | (cos θ_{1} - i sin θ_{1}) = - ¯ ¯¯ ¯ w \end{matrix}$
Hence, option $D$ is the correct answer.

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Let z and ω are two non-zero complex numbers such that |z|=|ω| and argz+argω=π, then z equal to

The correct option is B −¯¯¯ωFromthehelpofgivenquestionz=|z|(cosθ+isinθ)whereθ=zIfθ1=wthentanθ=π−θ1So,z=|w|(cos(π−θ1)+isin(π−θ1))=|w|(−cosθ1+isinθ1)=−|w|(cosθ1−isinθ1)=−¯¯¯¯wHence, option D is the correct answer.

Let $z$ and $ω$ are two non-zero complex numbers such that $| z | = | ω |$ and $arg z + arg ω = π,$ then $z$ equal to