Locus of a complex number satisfying z-5-4iz-3-2i-4 is arc of a circle

Z_0 ( 3+2i)z_0 (5 4i)=BDADe^iπ/2=i ⇒ z_0+3 2i=iz_0 5i 4 ⇒ z_0= 2 5i ⇒Radius AD=|5 4i ( 2 5i)| =|7+i|=√(50)=5√(2) Length of arc =34(Perimeter of circle) =34(2π× ...

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

Byju's Answer

Standard XII

Mathematics

Equation of Circle in Complex Form

Locus of a co...

Question

Locus of a complex number satisfying $arg (\frac{(z - 5 + 4 i)}{(z + 3 - 2 i)}) = - \frac{π}{4}$ is arc of a circle

whose radius is

5 \sqrt{2}

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

whose radius is

5

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

whose length of arc os

\frac{15 π}{\sqrt{2}}

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

whose centre is

- 2 - 5 i

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

Open in App

Solution

The correct option is D whose centre is $- 2 - 5 i$
$\frac{z_{0} - (- 3 + 2 i)}{z_{0} - (5 - 4 i)} = \frac{B D}{A D} e^{i π / 2} = i$
$\Rightarrow z_{0} + 3 - 2 i = i z_{0} - 5 i - 4$
$\Rightarrow z_{0} = - 2 - 5 i$
$\Rightarrow Radius A D = | 5 - 4 i - (- 2 - 5 i) |$
$= | 7 + i | = \sqrt{50} = 5 \sqrt{2}$
Length of arc $= \frac{3}{4}$ (Perimeter of circle)
$= \frac{3}{4} (2 π \times 5 \sqrt{2}) = \frac{15 π}{\sqrt{2}}$

Suggest Corrections

Similar questions

Q. Locus of a complex number satisfying

arg (\frac{(z - 5 + 4 i)}{(z + 3 - 2 i)}) = - \frac{π}{4}

is arc of a circle

Q. Locus of complex number satisfying

arg [\frac{(z - 5 + 4 i)}{(z + 3 - 2 i)}] = - \frac{π}{4}

is the arc of a circle

Q. Locus of complex number satisfying

arg [\frac{(z - 5 + 4 i)}{(z + 3 - 2 i)}] = - \frac{π}{4}

is the arc of a circle

Q. If z is complex number then interpret the locus of following in complex plane

A r g (z - a) = \frac{π}{3}

where

a = 3 + 4 i

Q. Assertion :There are exactly two complex numbers which satisfy the complex equations

| z - 4 - 5 i | = 4

and

A r g (z - 3 - 4 i) = \frac{π}{4}

simultaneously. Reason: A line cuts the circle in atmost two points.

Join BYJU'S Learning Program

Locus of a complex number satisfying arg((z−5+4i)(z+3−2i))=−π4 is arc of a circle

The correct option is D whose centre is −2−5iz0−(−3+2i)z0−(5−4i)=BDADeiπ/2=i ⇒z0+3−2i=iz0−5i−4 ⇒z0=−2−5i ⇒Radius AD=|5−4i−(−2−5i)| =|7+i|=√50=5√2 Length of arc =34(Perimeter of circle) =34(2π×5√2)=15π√2

Locus of a complex number satisfying $arg (\frac{(z - 5 + 4 i)}{(z + 3 - 2 i)}) = - \frac{π}{4}$ is arc of a circle