If 2z1-3z2 is a purely imaginary number- then - z1 - z2-z1 - z2 - -MP PET 1993-

As given, let 2z_1/3z_2= iy or z_1/z_2 = 3/2 iy, so that | z_1 z_2/z_1 + z_2 | = | z_1/z_2 1/z_1/z_2 + 1 | = | 3/2iy 1/3/2iy + 1 | = | 1 3/2 iy/1+ 3/2 ...

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

Byju's Answer

Standard XII

Mathematics

Purely Imaginary

If 2z1/3z2 is...

Question

If $\frac{2 z_{1}}{3 z_{2}}$ is a purely imaginary number, then $∣ ∣ \frac{z_{1} - z_{2}}{z_{1} + z_{2}} ∣ ∣$ =
[MP PET 1993]

3/2

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

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

2/3

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

4/9

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

Open in App

Solution

The correct option is B
1

As given, let $\frac{2 z_{1}}{3 z_{2}} = i y o r \frac{z_{1}}{z_{2}} = \frac{3}{2} i y,$ so that
$∣ ∣ \frac{z_{1} - z_{2}}{z_{1} + z_{2}} ∣ ∣ = ∣ ∣ ∣ ∣ \frac{\frac{z_{1}}{z_{2}} - 1}{\frac{z_{1}}{z_{2}} + 1} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ \frac{\frac{3}{2} i y - 1}{\frac{3}{2} i y + 1} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{1 - \frac{3}{2} i y}{1 + \frac{3}{2} i y} ∣ ∣ ∣ = 1 ∵ | z | = | ¯ z |$

Suggest Corrections

Similar questions

Q. If

\frac{2 z_{1}}{3 z_{2}}

is a purely imaginary number, then

∣ ∣ \frac{z_{1} - z_{2}}{z_{1} + z_{2}} ∣ ∣

=
[MP PET 1993]

Q. If

\frac{2 z_{1}}{3 z_{2}}

is a purely imaginary number, then

∣ ∣ \frac{z_{1} - z_{2}}{z_{1} + z_{2}} ∣ ∣

=
[MP PET 1993]

Q. If

\frac{2 z_{1}}{3 z_{2}}

is a purely imaginary number,then

∣ ∣ ∣ \frac{z_{1} - z_{2}}{z_{1} + z_{2}} ∣ ∣ ∣ =

Q. If

z_{1}, z_{2}

are complex numbers such that

\frac{2 z_{1}}{3 z_{2}}

is purely imaginary number, then find |

\frac{z_{1} - z_{2}}{z_{1} + z_{2}}

Q. If

{2 z}_{1} {/ 3 z}_{2}

is a purely imaginary number, then find the value of

| (z_{1} - z_{2}) / (z_{1} + z_{2}) |

Join BYJU'S Learning Program

If 2z13z2 is a purely imaginary number, then ∣∣z1−z2z1+z2∣∣ = [MP PET 1993]

The correct option is B 1 As given, let 2z13z2=iyorz1z2=32iy, so that ∣∣z1−z2z1+z2∣∣=∣∣ ∣∣z1z2−1z1z2+1∣∣ ∣∣=∣∣∣32iy−132iy+1∣∣∣=∣∣∣1−32iy1+32iy∣∣∣=1∵ |z|=|¯z|

If $\frac{2 z_{1}}{3 z_{2}}$ is a purely imaginary number, then $∣ ∣ \frac{z_{1} - z_{2}}{z_{1} + z_{2}} ∣ ∣$ =
[MP PET 1993]