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If z1, z2 and z3, z4 are 2 pairs of complex conjugate numbers, thenarg\left ( \frac{Z_{1}}{Z_{4}} \right )+arg\left ( \frac{Z_{2}}{Z_{3}} \right )equals:

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best_answer

It is given that,
z_1\ and\ z_2 are the complex conjugate so, z_2 = \overline{z_1}
Similarily, z_4 = \overline{z_3}

Now, arg\left ( \frac{Z_{1}}{Z_{4}} \right )+arg\left ( \frac{Z_{2}}{Z_{3}} \right )
\Rightarrow \arg (\frac{z_1}{z_4})(\frac{z_2}{z_3})
\\\Rightarrow \arg (\frac{z_1.\overline{z_1}}{z_3.\overline{z_3}})\\ \Rightarrow \arg (\frac{\left | z_1 \right |^2}{\left | z_3 \right |^2})
= 0 (since \frac{\left | z_1 \right |^2}{\left | z_3 \right |^2} is purely real)
 

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manish

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