Let ${z_1},{z_2},{z_3}$ be three complex numbers satisfying $\frac{1}{{{z_1}}} + \frac{1}{{{z_2}}} + \frac{1}{{{z_3}}} = 0.$ Let ${z_k} = {r_k}\left( {\cos {\alpha _k} + i\sin {\alpha _k}} \right)$ and ${\omega _k} = \frac{{\cos 2{\alpha _k} + i\sin 2\;{\alpha _k}}}{{{z_k}}}$ for $k = 1,2,3.$ If ${\omega _1},{\omega _2}$ and ${\omega _3}$ are the affixes of points ${A_1},{A_2}$ and ${A_3}$ respectively in the Argand plane, then $\Delta {A_1}{A_2}{A_3}$ has its

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Analyzing +4 | -1

Let

{z_1},{z_2},{z_3}

be three complex numbers satisfying

\frac{1}{{{z_1}}} + \frac{1}{{{z_2}}} + \frac{1}{{{z_3}}} = 0.

Let

{z_k} = {r_k}\left( {\cos {\alpha _k} + i\sin {\alpha _k}} \right)

and

{\omega _k} = \frac{{\cos 2{\alpha _k} + i\sin 2\;{\alpha _k}}}{{{z_k}}}

for

k = 1,2,3.

{\omega _1},{\omega _2}

and

{\omega _3}

are the affixes of points

{A_1},{A_2}

and

{A_3}

respectively in the Argand plane, then

\Delta {A_1}{A_2}{A_3}

has its

View answer and explanation

Correct option: B

Centroid at the origin

Option B (Centroid at the origin) is correct because the sum of the complex numbers representing the vertices is zero, implying the centroid is at the origin.

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

More Questions from COMPLEX NUMBERS