MyQuestionIcon

1

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

Definition of Functions

If |z-3|= m...

Question

If $| z - 3 | = m i n (| z - 1 |, | z - 5 |)$ then $R e (z)$ equals to

A

2

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

B

\frac{5}{2}

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

C

\frac{7}{2}

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

D

4

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

Open in App

Solution

The correct options are
A $2$
D $4$
Let $z = x + i y$
Hence either $| z - 3 | = | z - 1 |$
$(x - 1)^{2} + y^{2} = (x - 3)^{2} + y^{2}$
$x - 1 = \pm (x - 3)$
$x - 1 = - x + 3$
$x = 2$ ...(i)
Hence $R e (z) = 2$ .
OR
$| z - 3 | = | z - 5 |$
$(x - 3)^{2} + y^{2} = (x - 5)^{2} + y^{2}$
$(x - 3) = \pm (x - 5)$
$x - 3 = - x + 5$
$2 x = 8$
$x = 4$ .
$R e (z) = 4$ .

Suggest Corrections

thumbs-up

0

Similar questions

| z - 3 | = m i n {| z - 1 |, | z - 5 |}

R e (z)

| z - 2 | = min {| z - 1 |, | z - 5 |}

z

is a complex number, then possible value(s) of

R e (z)

| z - 2 | = min {| z - 1 |, | z - 5 |}

z

is a complex number, then possible value(s) of

R e (z)

Q. Assertion :If

z = \sqrt{3 + 4 i} + \sqrt{- 3 + 4 i}

, then principal arg of z i.e. arg (z) are

\pm \frac{π}{4}, \pm \frac{3 π}{4}

\sqrt{- 1} = i

. Reason: If z = A + iB, then

\sqrt{z} = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \sqrt{\frac{| z | + R e (z)}{2}} + i \sqrt{\frac{| z | - R e (z)}{2}} & , if B > 0 \sqrt{\frac{| z | + R e (z)}{2} - i \sqrt{\frac{| z | - R e (z)}{2}}} & , if B < 0 \end{matrix}

Given z is a complex number satisfying $z^{2} - z - | z |^{2} + \frac{64}{| z |^{5}} = 0$ and Re(z) $\neq \frac{1}{2}$ (where Re(z) denotes real part of z), then |z| is less than

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Definition of Function

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Definition of Functions

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon