If $| z_{1} | = | z_{2} | = | z_{3} | = | z_{4} |$ and $z_{1} + z_{2} + z_{3} + z_{4} = 0$ then the points $z_{1}, z_{2}, z_{3}, z_{4}$ in the Argand plane are the vertices of a

Trapezium

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

Rectangle

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

Square

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 Trapezium
As $| z_{1} | = | z_{2} | = | z_{3} | = | z_{4} |$ it represents a square or a rhombus.
$z_{1} = x + i y$
$z_{2} = x - i y$
$z_{3} = - x + i y$
$z_{4} = - x - i y$
from the above points it is clear that $| z_{1} | = | z_{2} | = | z_{3} | = | z_{4} | = \sqrt{(x^{2} + y^{2})}$
$| z_{1} - z_{2} | = | z_{2} - z_{3} | = | z_{3} - z_{4} | = | z_{4} - z_{1} |$ i.e., magnitude of sides is equal
$z_{1} + z_{2} + z_{3} + z_{4} = x + i y + x - i y - x + i y - x - i y = 0$
$∴$ The above points represents a square.

Suggest Corrections

Similar questions

The points $z_{1}, z_{2}, z_{3}, z_{4}$ in the complex plane are the vertices of a parallelogram taken in order, if and only if

Q. If

| z_{1} | = | z_{2} | = | z_{3} | = | z_{4} | = 1

and

z_{1} + z_{2} + z_{3} + z_{4} = 0

, then least value of the expression

E = | z_{1} - z_{2} |^{2} + | z_{2} - z_{3} |^{2} + | z_{3} - z_{4} |^{2} + | z_{4} - z_{1} |^{2}

Q. If

| z_{1} | = | z_{2} | = | z_{3} | = | z_{4} |

then the points representing

z_{1}, z_{2}, z_{3}, z_{4}

are

Q. Suppose

z_{1} + z_{2} + z_{3} + z_{4} = 0

and

| z_{1} | = | z_{2} | = | z_{3} | = | z_{4} | = 1 i f z_{1}, z_{2}, z_{3}, z_{4}

are the vertices of a quadrilateral, then the quadrilateral must be a

If | $z_{1} | = | z_{2} | = | z_{3} | = | z_{4} | = 1$ and $z_{1} + z_{2} + z_{3} + z_{4} = 0$
then least value of the expression
$E = | z_{1} - z_{2} |^{2} + | z_{2} - z_{3} |^{2} + | z_{3} - z_{4} |^{2} + | z_{4} - z_{1} |^{2}$ is

Join BYJU'S Learning Program

If |z1|=|z2|=|z3|=|z4| and z1+z2+z3+z4=0 then the points z1,z2,z3,z4 in the Argand plane are the vertices of a

If $| z_{1} | = | z_{2} | = | z_{3} | = | z_{4} |$ and $z_{1} + z_{2} + z_{3} + z_{4} = 0$ then the points $z_{1}, z_{2}, z_{3}, z_{4}$ in the Argand plane are the vertices of a