If z1- z2- and z3- z4 are conjugate complex pairs then z3z2-

The correct option is B z_1/z_4 We have arg (z_3z_2)+arg #10;(z̅_̅3̅z̅_̅2̅)=0 ⇒ #160;arg (z_3z_2)+arg #10;(z_4z_1)=0 ⇒ #160;arg (z_ ...

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Byju's Answer

Standard XII

Mathematics

Properties of Argument

If z1, z2, ...

Question

If $(z_{1}, z_{2})$ , and $(z_{3}, z_{4})$ are conjugate complex pairs then $arg (\frac{z_{3}}{z_{2}}) =$

arg \frac{z_{1}}{z_{4}}

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arg \frac{z_{4}}{z_{1}}

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arg \frac{z_{2}}{z_{4}}

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arg \frac{z_{1}}{z_{3}}

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Solution

The correct option is B $arg \frac{z_{1}}{z_{4}}$
We have $a r g (\frac{z_{3}}{z_{2}}) + a r g (\frac{_{3}}{_{2}}) = 0$
$\Rightarrow a r g (\frac{z_{3}}{z_{2}}) + a r g (\frac{z_{4}}{z_{1}}) = 0$
$\Rightarrow a r g (\frac{z_{3}}{z_{2}}) = - a r g (\frac{z_{4}}{z_{1}})$

$\Rightarrow a r g (\frac{z_{3}}{z_{2}}) = a r g (\frac{z_{1}}{z_{4}})$

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Similar questions

If $z_{1}, z_{2} and z_{3}, z_{4}$ are two pairs of conjugate complex numbers, prove that $a r g (\frac{z_{1}}{z_{4}}) + a r g (\frac{z_{2}}{z_{3}}) = 0.$

If $(z_{1}, z_{2})$ and $(z_{3}, z_{4})$ are two pairs of conjugate complex numbers, then show that

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Q. If

z_{1}, z_{2}

and

z_{3}, z_{4}

are two pairs of conjugate complex numbers, then

a r g (\frac{z_{1}}{z_{4}}) + a r g (\frac{z_{2}}{z_{3}})

equals

If | $z_{1} | = | z_{2} | = | z_{3} | = | z_{4} | = 1$ and $z_{1} + z_{2} + z_{3} + z_{4} = 0$
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If (z1, z2), and (z3, z4) are conjugate complex pairs then arg(z3z2)=

The correct option is B argz1z4We have arg(z3z2)+arg(¯z3¯z2)=0⇒arg(z3z2)+arg(z4z1)=0⇒arg(z3z2)=−arg(z4z1) ⇒arg(z3z2)=arg(z1z4)

If $(z_{1}, z_{2})$ , and $(z_{3}, z_{4})$ are conjugate complex pairs then $arg (\frac{z_{3}}{z_{2}}) =$