QJEEM22Ma07be: JEE Main 2022 Mathematics - Class 11 JEEM22Ma07be Solution: If z = x + i y satisfies

Question

Verified Solution • 2025–26 Session moderate

If $z = x + i y$ satisfies $| z | - 2 = 0$ and $| z - i | - | z + 5 i | = 0$ , then :

Accepted Answer

$| z - i | = | z + 5 i |$

So, $z$ lies on $⊥^{r}$ bisector of $(0, 1)$ and $(0, - 5)$

i.e., line $y = - 2$

as $| z | = 2$

$\Rightarrow z = - 2 i$

$x = 0$ and $y = - 2$

so, $x + 2 y + 4 = 0$

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