If the complex numbers $z_{1}, z_{2}, z_{3}$ represent the vertices of an equilateral triangle such that $|z_{1}| = |z_{2}| = |z_{3}|$ , then $z_{1} + z_{2} + z_{3}$ equal:

$0$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$1$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$- 1$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
$0$

Explanation for the correct option.
Given, $z_{1}, z_{2}, z_{3}$ are the vertices of an equilateral triangle.
Assume $O$ be the origin then,
$z_{1} = O A, z_{2} = O B, z_{3} = O C$
Here, $O$ is the circumcenter of the triangle.
$\Rightarrow z_{1} + z_{2} + z_{3} = 0$
Hence, option A is correct.

Suggest Corrections

Similar questions

z_{1}, z_{2}, z_{3}

| z_{1} | = | z_{2} | = | z_{3} |,

z_{1} + z_{2} + z_{3} =

z_{1}, z_{2}, z_{3}

| z_{1} | = | z_{2} | = | z_{3} |

z_{1} + z_{2} + z_{3} = 0

z_{1}, z_{2}, z_{3}

| z_{1} | = | z_{2} | = | z_{3} |

z_{1}, z_{2}

z_{3}

| z_{1} | = | z_{2} | = | z_{3} |

z_{1} + z_{2} + z_{3} = 0

z_{1}, z_{2}, z_{3}

\frac{1}{z_{1} - z_{2}} + \frac{1}{z_{2} - z_{3}} + \frac{1}{z_{3} - z_{1}} = 0

Join BYJU'S Learning Program