"Let z1 and z2 be two complex numbers such that ${\overline z _1} = i{\overline z _2}$ and $\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi$. Then :"

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$\because$ ${{{z_1}} \over {{z_2}}} = - i \Rightarrow {z_1} = - i{z_2}$

$\Rightarrow \arg ({z_1}) = - {\pi \over 2} + \arg ({z_2})$ ..... (i)

Also $\arg ({z_1}) - \arg ({\overline z _2}) = \pi$

$\Rightarrow \arg ({z_1}) + \arg ({z_2}) = \pi$ ..... (ii)

From (i) and (ii), we get

$\arg ({z_1}) = {\pi \over 4}$ and $\arg ({z_2}) = {{3\pi } \over 4}$

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Let z₁ and z₂ be two complex numbers such that ${\overline z _1} = i{\overline z _2}$ and $\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi$. Then :

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Let z1 and z2 be two complex numbers such that ${\overline z _1} = i{\overline z _2}$ and $\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi$. Then :

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Let z₁ and z₂ be two complex numbers such that ${\overline z _1} = i{\overline z _2}$ and $\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi$. Then :