SATHEE: Complex Numbers 2 Question 35

Complex Numbers 2 Question 35

36.

If the complex numbers, $z_{1}, z_{2}$ and $z_{3}$ represent the vertices of an equilateral triangle such that $| z_{1} | = | z_{2} | = | z_{3} |$ , then $z_{1} + z_{2} + z_{3} = 0$ .

(1984, 1M)

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Answer:

Correct Answer: 36. True

Solution:

Since, $z_{1}, z_{2}, z_{3}$ are vertices of equilateral triangle and $| z_{1} | = | z_{2} | = | z_{3} |$

$\Rightarrow z_{1}, z_{2}, z_{3}$ lie on a circle with centre at origin.

$\Rightarrow$ Circumcentre $=$ Centroid

$\begin{array}{lrl} \Rightarrow & 0 & = \frac{z_{1} + z_{2} + z_{3}}{3} \\ ∴ & z_{1} + z_{2} + z_{3} & = 0 \end{array}$

Complex Numbers 2 Question 35

36.

Answer:

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Complex Numbers 2 Question 35

36.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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