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>>Class 11
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>>Complex Numbers
>> $State true or false:The complex numbers$

Question

State true or false:
The complex numbers $z = x + i y$ which satisfy the equation $∣ ∣ ∣ ∣ ∣ \frac{z - 5 i}{z + 5 i} ∣ ∣ ∣ ∣ ∣ = 1$ lie on the axis of $Y$ .

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Updated on : 2022-09-05

Solution

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Correct option is A)

$∣ ∣ ∣ ∣ ∣ \frac{z - 5 i}{z + 5 i} ∣ ∣ ∣ ∣ ∣ = 1$ or
$∣ x + i y - 5 i ∣^{2} = ∣ x + i y + 5 i ∣^{2}$
or $x^{2} + (y - 5)^{2} = x^{2} + (y + 5)^{2}$
or $20 y = 0$ or $y = 0$

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