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

Geometrical Representation of Algebra of Complex Numbers

Let z 1 , z...

Question

Let $z_{1}, z_{2}$ be two fixed complex numbers in the argand plane and $z$ be an arbitrary point satisfying $| z - z_{1} | + | z - z_{2} | = k,$ if $| z_{1} - z_{2} | < k$ , then the locus of $z$ will be represent

An ellipse

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

A straight line joining

z_{1}

and

z_{2}

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

A parabola

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

A bisector of the line segment joining

z_{1}

and

z_{2}

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

Open in App

Solution

The correct option is D An ellipse
We know that
$| z - z_{1} | + | z - z_{2} | = k$ will represent an ellipse, if $| z_{1} - z_{2} | < k$ .
Hence, the equation represents an ellipse.

Suggest Corrections

Similar questions

z_{1}, z_{2}

z

| z - z_{1} | + | z - z_{2} | = | z_{1} - z_{2} |

z

| z - z_{1} | + | z - z_{2} | = k (> | z_{1} - z_{2} |)

z

z_{1}

z_{2}

If $| z - z_{1} | + | z + z_{2} |$ = $λ, λ \in R^{+}, z_{1}, z_{2}$ are fixed complex numbers, represents an ellipse, then:

Z_{1} = 2 + 3 i

z_{2} = 3 + 4 i

| z - z_{1} |^{2} + | z - z_{2} |^{2} = | z_{1} - z_{2} |^{2}

z_{1} = 2 + 3 i

z_{2} = 3 + 4 i

z

{| z - z_{1} |}^{2} + {| z - z_{2} |}^{2} = {| z_{1} - z_{2} |}_{1}^{2}

Join BYJU'S Learning Program