If {z_1}, {z_2} and {z_3}, {z_4} are two pair | vedclass

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(A) Given that ${z_1}, {z_2}$ are conjugate,so ${z_2} = \overline{z_1}$.Given that ${z_3}, {z_4}$ are conjugate,so ${z_4} = \overline{z_3}$.We need to

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(A) Given that ${z_1}, {z_2}$ are conjugate,so ${z_2} = \overline{z_1}$.Given that ${z_3}, {z_4}$ are conjugate,so ${z_4} = \overline{z_3}$.We need to evaluate $arg\left( \frac{z_1}{z_4} \right) + arg\left( \frac{z_2}{z_3} \right)$.Using the property $arg(a) + arg(b) = arg(ab)$,we get:$arg\left( \frac{z_1}{z_4} \cdot \frac{z_2}{z_3} \right) = arg\left( \frac{z_1 z_2}{z_3 z_4} \right)$.Since ${z_1} \overline{z_1} = |z_1|^2$,we have ${z_1} {z_2} = |z_1|^2$ and ${z_3} {z_4} = |z_3|^2$.Substituting these,we get $arg\left( \frac{|z_1|^2}{|z_3|^2} \right) = arg\left( \left| \frac{z_1}{z_3} \right|^2 \right)$.Since $\left| \frac{z_1}{z_3} \right|^2$ is a positive real number,its argument is $0$.

If ${z_1}, {z_2}$ and ${z_3}, {z_4}$ are two pairs of conjugate complex numbers,then $arg\left( \frac{z_1}{z_4} \right) + arg\left( \frac{z_2}{z_3} \right)$ equals:

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