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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)|
 
 

Grade:11

1 Answers

Arun
25750 Points
5 years ago
Dear kanish
 
 

|(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 

 

 

Regards

Arun

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