Question

find square root -8-6i

Answer 1

HEY MATE ,
HERE IS YOUR ANSWER
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LET
$\sqrt{ - 8 - 6i} = a + ib$
by squaring both the sides
$- 8 - 6i = {a}^{2} - {b}^{2} + 2ab$
NOW,

on comparing real part to real and imaginary part to imaginary
$- 8 = {a}^{2} - {b}^{2} \: \: \: \: - (i)$
$- 6 = 2ab$
$b = - \frac{3}{a}$

putting value in eq. (i)
$- 8 = {a}^{2} - {(\frac{ - 3}{a})}^{2}$
${a}^{4} - 9 + 8 {a}^{2} = 0$
${a}^{4} - 9 {a}^{2} + 1 {a}^{2} - 9 = 0$

${a}^{2} ( {a}^{2} - 9) + 1( {a}^{2} - 9) = 0$
$( {a}^{2} - 9)( {a}^{2} + 1) = 0$
${a}^{2} = 9 \: \: \: \: or \\ a = \binom{ + }{ - } 3$
so,
$b = \binom{ - }{ + } 1$
answer=
$= \binom{ + }{ - } (3 - 1i)$

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Answer 2

see in attachment mate

hope it's helps you ❤️