If z be a complex number such that - z-2 - -2- z-1 - then - z - 2 - Rez- where - is-

The correct option is A 43 | z 2 | =2| z 1 | Put z=x+iy ⇒ |(x 2)+iy|=2|(x 1)+iy| ⇒ (x 2)^2+y^2=4(x 1)^2+4y^2 ⇒x^2+y^2=43x⇒ |z|^2 ...

592

You visited us 592 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Modulus of a Complex Number

If z be a c...

Question

If $z$ be a complex number such that $| z - 2 | = 2 | z - 1 |$ , then ${| z |}^{2} = λ R e (z)$ , where $λ$ is-

\frac{4}{3}

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

\frac{2}{3}

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

\frac{1}{3}

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

1

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

Open in App

Solution

The correct option is A $\frac{4}{3}$
$| z - 2 | = 2 | z - 1 |$
Put $z = x + i y$
$\Rightarrow | (x - 2) + i y | = 2 | (x - 1) + i y |$
$\Rightarrow (x - 2)^{2} + y^{2} = 4 (x - 1)^{2} + 4 y^{2}$
$\Rightarrow x^{2} + y^{2} = \frac{4}{3} x \Rightarrow | z |^{2} = \frac{4}{3} R e (z)$

Suggest Corrections

Similar questions

If $z_{1}, z_{2}$ are complex numbers such that $z_{1}^{3} - 3 z_{1} z_{2}^{2}$ = 2 and $3 z_{1}^{2} z_{2} - z_{2}^{3}$ = 11 then $| z_{1}^{2} + z_{2}^{2} |$ =

Q. If z₁, z₂, z₃ are complex numbers such that

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

, then find the value of

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

Q. If

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

be the complex numbers such that

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

and

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

, then

\frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} = 0

Q. If

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

non-zero, non-collinear complex numbers such that

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

then the points

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

lie

Q. Let

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

be complex numbers such that

z_{1}^{2} + z_{2}^{2} + z_{3}^{2} = z_{1} z_{2} + z_{2} z_{3} + z_{3} z_{1}

and

| z_{1} + z_{2} + z_{3} | = 21.

Given that

| z_{1} - z_{2} | = 2 \sqrt{3}, | z_{1} | = 3 \sqrt{3},

then the value of

| z_{2} |^{2} + | z_{3} |^{2}

Join BYJU'S Learning Program

If z be a complex number such that |z−2|=2|z−1|, then |z|2=λRe(z), where λ is-

The correct option is A 43|z−2|=2|z−1|Put z=x+iy ⇒|(x−2)+iy|=2|(x−1)+iy|⇒(x−2)2+y2=4(x−1)2+4y2⇒x2+y2=43x⇒|z|2=43Re(z)

If $z$ be a complex number such that $| z - 2 | = 2 | z - 1 |$ , then ${| z |}^{2} = λ R e (z)$ , where $λ$ is-

The correct option is A $\frac{4}{3}$
$| z - 2 | = 2 | z - 1 |$
Put $z = x + i y$
$\Rightarrow | (x - 2) + i y | = 2 | (x - 1) + i y |$
$\Rightarrow (x - 2)^{2} + y^{2} = 4 (x - 1)^{2} + 4 y^{2}$
$\Rightarrow x^{2} + y^{2} = \frac{4}{3} x \Rightarrow | z |^{2} = \frac{4}{3} R e (z)$