Question

# If $${z}_{1},{z}_{2},{z}_{3}$$ be the complex numbers such that $${z}_{1}+{z}_{2}+{z}_{3}=0$$ and $$\left| { z }_{ 1 } \right| =\left| { z }_{ 2 } \right| =\left| { z }_{ 3 } \right| =1$$, then $$\dfrac { 1 }{ { z }_{ 1 } } +\dfrac { 1 }{ { z }_{ 2 } } +\dfrac { 1 }{ { z }_{ 3 } } =0$$

A
True
B
False

Solution

## The correct option is A TrueTrue.|z|=|$$\bar{z}$$|$$|z|=1\Rightarrow z\cdot \bar z=1$$$$\left ( \dfrac{1}{z} \right )$$=$$\bar{z}$$$$z_1+z_2+z_3=0$$$$\Rightarrow \bar{ z_1}+\bar{z}_2+\bar{z}_3=0$$$$\Rightarrow \dfrac{1}{z_1}+\dfrac{1}{z_2}+\dfrac{1}{z_3}=0$$Mathematics

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