If z 1- z 2 andz 3- z 4 are two pairs of conjugate complex numbers- z 1- z 4- z 2- z 3 then equalsA- 0B- -2C- 3 -2D- -

We have z_1 = z̅_1 and z_4 = z̅_3 Therefore z_1 z_2 = |z_1|^2 and z_3 z_4=|z_3|^2 Now arg (z_1/z_4 )+arg (z_2/z_3 )=arg (z_1z_2/z_4z_3 ) arg (|z_1|^2 ...

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Byju's Answer

Standard XII

Mathematics

Properties of Argument

If z 1, z 2 a...

Question

If $z_{1}, z_{2} a n d z_{3}, z_{4}$ are two pairs of conjugate complex numbers, $a r g (\frac{z_{1}}{z_{4}}) + a r g (\frac{z_{2}}{z_{3}})$ then equals

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Solution

The correct option is A
$W e h a v e z_{1} = {¯ z}_{1} a n d z_{4} = {¯ z}_{3} T h e r e f o r e z_{1} z_{2} = | z_{1} |^{2} a n d z_{3} z_{4} = | z_{3} |^{2} N o w a r g (\frac{z_{1}}{z_{4}}) + a r g (\frac{z_{2}}{z_{3}}) = a r g (\frac{z_{1} z_{2}}{z_{4} z_{3}}) a r g (\frac{| z_{1} |^{2}}{| z_{3} |^{2}}) = a r g ({∣ ∣ \frac{z_{1}}{z_{3}} ∣ ∣}^{2}) 0 (∵ A r g u m e n t o f p o s i t i v e r e a l n u m b e r i s z e r o)$

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Similar questions

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If z1,z2andz3,z4 are two pairs of conjugate complex numbers, arg(z1z4)+arg(z2z3) then equals

The correct option is A We havez1=¯z1 and z4=¯z3Thereforez1 z2=|z1|2 and z3 z4=|z3|2Now arg(z1z4)+arg(z2z3)=arg(z1z2z4z3)arg(|z1|2|z3|2)=arg(∣∣z1z3∣∣2)0(∵ Argument of positive real number is zero)

If $z_{1}, z_{2} a n d z_{3}, z_{4}$ are two pairs of conjugate complex numbers, $a r g (\frac{z_{1}}{z_{4}}) + a r g (\frac{z_{2}}{z_{3}})$ then equals