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

Byju's Answer

Standard XII

Mathematics

Section Formula Using Complex Numbers

Let Z1=2+3i...

Question

Let $Z_{1} = 2 + 3 i$ and $z_{2} = 3 + 4 i$ be two points on the complex plane. Then the set of complex numbers z satisfying $| z - z_{1} |^{2} + | z - z_{2} |^{2} = | z_{1} - z_{2} |^{2}$ repesents

A straight line

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

A point

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

A circle

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

A pair of straight lines

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

Open in App

Solution

The correct option is C A circle
Putting z = x +iy,

$(x - 2)^{2}$ + $(y - 3)^{2}$ + $(x - 3)^{2}$ + $(y - 4)^{2}$ = $\sqrt{2}$

Expanding the above expression gives us a circle.

Hence, option C is correct.

Suggest Corrections

Similar questions

Q. If

z_{1} = 2 + 3 i

and

z_{2} = 3 + 4 i

be two points on the complex plane. Then, the set of complex number

z

is satisfying

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

represents

Q. Indicate the point of the complex plane

z

which satisfy the following equation.
Prove that

| z_{1} + z_{2} |^{2} + | z_{1} - z_{2} |^{2} = 2 (| z_{1} |^{2} + | z_{2} |^{2})

for any two complex numbers

z_{1}

and

z_{2} .

Q. Let

z_{1}, z_{2}

be two fixed complex numbers in the Argand plane and

z

be an arbitary point satisfying

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

. Then the locus of

z

will be

Q. 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,

| z_{1} - z_{2} | < k

, then the locus of

z

will be represent

Q. Let

z_{1} = 6 + i

and

z_{2} = 4 - 3 i

. Let

Z

be a complex number such that the

a r g (\frac{z - z_{1}}{z_{2} - z}) = \frac{π}{2}

, then

z

satisfies the realtion

Join BYJU'S Learning Program

Let Z1=2+3i and z2=3+4i be two points on the complex plane. Then the set of complex numbers z satisfying |z−z1|2+|z−z2|2=|z1−z2|2 repesents

The correct option is C A circlePutting z = x +iy, (x−2)2 + (y−3)2 + (x−3)2 + (y−4)2 = √2Expanding the above expression gives us a circle.Hence, option C is correct.

Let $Z_{1} = 2 + 3 i$ and $z_{2} = 3 + 4 i$ be two points on the complex plane. Then the set of complex numbers z satisfying $| z - z_{1} |^{2} + | z - z_{2} |^{2} = | z_{1} - z_{2} |^{2}$ repesents

The correct option is C A circle
Putting z = x +iy,

$(x - 2)^{2}$ + $(y - 3)^{2}$ + $(x - 3)^{2}$ + $(y - 4)^{2}$ = $\sqrt{2}$

Expanding the above expression gives us a circle.

Hence, option C is correct.