Let $A = \frac{2}{\sqrt{3}} e^{- i \frac{π}{6}}$ , $B = \frac{2}{\sqrt{3}} e^{i \frac{π}{2}}$ , $C = \frac{2}{\sqrt{3}} e^{- \frac{i 5 π}{6}}$ be three points forming a triangle ABC in the Gaussian plane then triangle ABC is

Equilateral Triangle

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Isosceles

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Scalene

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None of these

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Solution

The correct option is A Equilateral Triangle
Plotting the Points,
$z = r e^{i θ}$ implies
r is the distance of point from origin & $^{'} θ^{'}$ is the angle made by the position vector of the point with +ve x-axis.
$∴$ Thus clearly, the triangle formed is an equilateral triangle $\Rightarrow$ all angles equal to $60^{\circ}$ .

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Similar questions

A = \frac{2}{\sqrt{3}} e^{- i \frac{π}{6}}, B = \frac{2}{\sqrt{3}} e^{i \frac{π}{2}}, C = \frac{2}{\sqrt{3}} e^{- \frac{5 π}{6}}

\frac{2}{\sqrt{3}} e^{- i \frac{π}{6}}

\frac{2}{\sqrt{3}} e^{i \frac{π}{2}}

\frac{2}{\sqrt{3}} e^{- i \frac{5 π}{6}}

A (\frac{2}{\sqrt{3}} e^{i π / 2}), B (\frac{2}{\sqrt{3}} e^{- i π / 6})

C (\frac{2}{\sqrt{3}} e^{- i 5 π / 6}) .

P

A P^{2} + B P^{2} + C P^{2} =

A (\frac{2}{\sqrt{3}} e^{i π / 2}), B (\frac{2}{\sqrt{3}} e^{- i π / 6}), C (\frac{2}{\sqrt{3}} e^{- i 5 π / 6})

P

A P^{2} + B P^{2} + C P^{2} =

A = \frac{2}{3} e^{\frac{i π}{2}}, B = \frac{2}{3} e^{\frac{i π}{6}}, C = \frac{2}{3} e^{\frac{i 5 π}{6}}

△ A B C

△ A B C

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