# Find the square roots of $9-12i$  Option 1) $\pm (2\sqrt3 - \sqrt 3 \:i)$ Option 2) $\pm (3 + 2i)$ Option 3) $\pm (\sqrt3 - 2\sqrt 3 \:i)$ Option 4) $\pm (3 - 2i)$

As learnt in concept

Definition of Complex Number -

$z=x+iy, x,y\epsilon R$  & i2=-1

- wherein

Real part of z = Re (z) = x & Imaginary part of z = Im (z) = y

$\sqrt{9-12i}= x+iy$

$9-12i= (x^{2}-y^{2})+2ixy$

$(x^{2}-y^{2})=9\: \: and \: \: xy=-6$

here, $x= 2\sqrt3\: \: and \: \: y= -\sqrt3$

Thus square root = $\pm (2\sqrt3- \sqrt 3i)$

Option 1)

$\pm (2\sqrt3 - \sqrt 3 \:i)$

Correct option

Option 2)

$\pm (3 + 2i)$

Incorrect option

Option 3)

$\pm (\sqrt3 - 2\sqrt 3 \:i)$

Incorrect option

Option 4)

$\pm (3 - 2i)$

Incorrect option

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