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Let $z= -12-5i$ and $w= 2\sqrt{11}+iy$ such that z and w both are equidistant from origin then y equals $\left ( Where\; y\epsilon R \right )$

Option 1)
$2\sqrt{5}$

Option 2)
$3\sqrt{5}$

Option 3)
$4\sqrt{5}$

Option 4)
$5\sqrt{5}$

Answers (1)

$\because$ z & w are equidistant from origin so $\left |z \right |=\left | w \right |$

$\Rightarrow \: \sqrt{144+25}=\sqrt{44+y^{2}}$

$\Rightarrow \: \sqrt{169}=\sqrt{44+y^{2}}$

$\Rightarrow \: 169=44+y^{2}$

$\Rightarrow \: y^{2}=125$

$\Rightarrow \: y=\pm 5\sqrt{5}$

$\therefore$ Option (D)

Definition of Modulus of z(Complex Number) -

$\left | z \right |=\sqrt{a^{2}+b^{2}}$ is the distance of z from origin in Argand plane

- wherein

Real part of z = Re (z) = a & Imaginary part of z = Im (z) = b

Option 1)

$2\sqrt{5}$

This is incorrect

Option 2)

$3\sqrt{5}$

This is incorrect

Option 3)

$4\sqrt{5}$

This is incorrect

Option 4)

$5\sqrt{5}$

This is correct

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