Find complex number $z$ satisfying the equation $| z - 4 |$ = $| z - 12 |$ .

2 + 3 i

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4

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8

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None of these

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Solution

The correct option is C $8$
Given equation is $| z - 4 |$ = $| z - 12 |$

Let $z = x + i y$ , then

$(x - 4)^{2} + y^{2} = (x - 12)^{2} + y^{2}$

$⟹ x^{2} - 8 x + 16 = x^{2} - 24 x + 144$

$⟹ 16 x = 128$

Hence $x = 8$ .

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Similar questions

∣ ∣ \frac{z - 12}{z - 8 i} ∣ ∣ = \frac{5}{3}, ∣ ∣ \frac{z - 4}{z - 8} ∣ ∣ = 1

Find the complex number z satisfying the equations $∣ ∣ \frac{z - 12}{z - 8 i} ∣ ∣$ = $\frac{5}{3}$ , $∣ ∣ \frac{z - 4}{z - 8} ∣ ∣$ =1

z

∣ ∣ ∣ \frac{z - 4}{z - 8} ∣ ∣ ∣ = 1

| z | = 10

∣ ∣ ∣ \frac{z - 12}{z - 8 i} ∣ ∣ ∣ = \frac{5}{3}

∣ ∣ ∣ \frac{z - 4}{z - 8} ∣ ∣ ∣ = 1

Find the complex numbers $z$ which simultaneously satisfy the equations

$∣ ∣ ∣ \frac{z - 12}{z - 8 i} ∣ ∣ ∣ = \frac{5}{3}$ and $∣ ∣ ∣ \frac{z - 4}{z - 8} ∣ ∣ ∣ = 1$ .

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