You visited us 1 times! Enjoying our articles? Unlock Full Access!

Distance Formula

If complex nu...

Question

If complex numbers $z_{1}, z_{2}, z_{3}$ are the vertices of a triangle, then the complex number $z$ which makes the triangle a parallelogram is given by

z_{1} + z_{2} - z_{3}

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

z_{1} + z_{3} - z_{2}

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

z_{2} + z_{3} - z_{1}

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

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

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

Open in App

Solution

The correct options are
A $z_{1} + z_{2} - z_{3}$
B $z_{1} + z_{3} - z_{2}$
C $z_{2} + z_{3} - z_{1}$
Consider C
$z_{1} + z_{4}$
$= z_{2} + z_{3}$
Hence $z_{1} - z_{2} = z_{3} - z_{4}$
Hence $z_{4}$ can form a parallelogram.
Consider B
$z_{2} + z_{4}$
$= z_{1} + z_{3}$
Hence
$z_{2} - z_{1} = z_{3} - z_{4}$
Hence it forms a parallelogram. ...(order of vertices changed).
Consider A
$z_{3} + z_{4}$
$= z_{1} + z_{2}$
Hence
$z_{3} - z_{1} = z_{2} - z_{4}$
Hence it forms a parallelogram. ...(order of vertices changed).
Hence the answers are A,B,C.

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} | = ∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ ∣ = 1

| z_{1} + z_{2} + z_{3} |

z_{1}, z_{2}

z_{3}

\frac{z_{1} - z_{3}}{z_{2} - z_{3}} = \frac{1 - i \sqrt{3}}{2}

z_{1}, z_{2}

z_{3}

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

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

| z_{3} |

∣ ∣ ∣ \frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} ∣ ∣ ∣ = 1,

| 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

Join BYJU'S Learning Program