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  • If z1, z2 and z3, z4 are two pairs of conjugate complex numbers, then find arg⁡(z_1/z_4 )+arg⁡(z_2/z_3 )

If z1, z2 and z3, z4 are two pairs of conjugate complex numbers, then find arg\left ( \frac{z_1}{z_4} \right )+arg\left ( \frac{z_2}{z_3} \right )

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z_1 and z_2  are conjugate complex numbers. 

The negative side of the real axis = r_1 (cos\theta-isin \theta)

=r_1\left ( \cos\left ( -\theta_1 \right )+i\sin\left (- \theta_1 \right ) \right )

Similarly, z_3=r_2\left ( \cos\left ( \theta_2 \right )-i\sin\left ( \theta_2 \right ) \right )

z_4=r_2\left ( \cos\left ( -\theta_2 \right )+i\sin\left (- \theta_2 \right ) \right )

arg \left ( \frac{z_1}{z_4} \right )+arg \left ( \frac{z_2}{z_3} \right )=arg(z_1)-arg(z_4)+ arg(z_2)- arg(z_3)??

=\theta_1-(-\theta_2)+(-\theta_1)-\theta_2=0

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infoexpert21

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