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if arg(z1/z2)=p/2 then find the value of |(z1+z2)/z1-z2)|

if arg(z1/z2)=p/2 then find the value of |(z1+z2)/z1-z2)|

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2 Answers

jitender lakhanpal
62 Points
10 years ago

|(z1+z2)/z1-z2)| = 1


|(z1+z2)|2  = |z1|2   + |z1|2  +  2|z1||z2|cos (θ1 -θ2)

and
|(z1-z2)|2  = |z1|2   + |z1|2    - 2|z1||z2|cos (θ1 -θ2)

where  θ1 and θ2   are arguments of z1 and z2


θ1 -θ2 = pie/2       so  cos (θ1 -θ2) = 0

so both of them are equal

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Thanks and Regards

Jitender

(askIITians expert)

Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

|(z1+z2)/z1-z2)| = 1
|(z1+z2)|2 = |z1|2 + |z1|2 + 2|z1||z2|cos (θ1 -θ2)
and
|(z1-z2)|2 = |z1|2 + |z1|2 - 2|z1||z2|cos (θ1 -θ2)
where θ1 and θ2 are arguments of z1 and z2
θ1 -θ2 = pie/2 so cos (θ1 -θ2) = 0
so both of them are equal

Thanks and Regards

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