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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
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B
False
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Solution

The correct option is A True
True.

|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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