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 ...

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Byju's Answer

Standard XIII

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]

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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
$∣ ∣ \frac{z_{1} - z_{2}}{z_{1} + z_{2}} ∣ ∣ = ∣ ∣ ∣ ∣ \frac{\frac{z_{1}}{z_{2}} - 1}{\frac{z_{1}}{z_{2}} + 1} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ \frac{\frac{3}{2} i y - 1}{\frac{3}{2} i y + 1} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{1 - \frac{3}{2} i y}{1 + \frac{3}{2} i y} ∣ ∣ ∣ = 1 ∵ | z | = | ¯ z |$

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Similar questions

Q. If

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

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

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[MP PET 1993]

Q. If

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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]