Where does z lie- if - z-5i z-5i - -1-

We have [ | z 5i / z+5i #160; | =1; | z 5i | =| z+5i | #160; ] So, z lies on #160; real axis which is perpendic ...

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Modulus of a Complex Number

Where does ...

Question

Where does $z$ lie, if $∣ ∣ ∣ \frac{z - 5 i}{z + 5 i} ∣ ∣ ∣ = 1$ .

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Solution

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z = x + i y

∣ ∣ ∣ \frac{z - 5 i}{z + 5 i} ∣ ∣ ∣ = 1

z = x + i y

∣ ∣ ∣ \frac{z - 5 i}{z + 5 i} ∣ ∣ ∣ = 1

z = x + i y

∣ ∣ ∣ \frac{z - 5 i}{z + 5 i} ∣ ∣ ∣ = 1

z = x + i y

\frac{| z - 5 i |}{| z + 5 i |} = 1

If $∣ ∣ \frac{z - 5 i}{z + 5 i} ∣ ∣ = 1$ , prove that $z$ is real.

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