For any complex numbers z,z1 and z2 prove that: (i) arg(¯z)=−arg(z) – InterviewSolution

1.	For any complex numbers z,z1 and z2 prove that: (i) arg(¯z)=−arg(z) (ii) arg(z1z2)=arg(z1)+arg(z2) (iii) arg(z1¯z2)=arg(z1)−arg(z2) (iv) arg(z1z2)=arg(z1)−arg(z2)
Answer» For any complex numbers $z, z_{1}$ and $z_{2}$ prove that: (i) $a r g (¯ z) = - a r g (z)$ (ii) $a r g (z_{1} z_{2}) = a r g (z_{1}) + a r g (z_{2})$ (iii) $a r g (z_{1}_{2}) = a r g (z_{1}) - a r g (z_{2})$ (iv) $a r g (\frac{z_{1}}{z_{2}}) = a r g (z_{1}) - a r g (z_{2})$

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