Grade 12th passAlgebra
How to find modulus |z| when |z-4|/|z-8|=1 and |z|/|z-2|=3/2
1 Answer
Vikas TU
let z = x + iy
put it in the given modulus:|z-4|/|z-8|=1
or
|z-4| = |z-8|
root[(x-y)^2 + y^2] = root[(x -8)^2 + y^2]
Squaring both sides and solving u will get,
(x – 4 + x – 8) (x – 4 – x + 8) = 0
(2x – 12 ) = 0
x = 6........................(1)
Now,
|z|/|z-2|=3/2
after solving u will get,
(2x)^2 – [3(x-2)]^2 = 5y^2
put here x = 6
y = 0
z = 6 (pure real)
|z| = 6
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