- 8 - 6i = - Vidyadip

MCQ

$\sqrt { - 8 - 6i} = $

A
$1 \pm 3i$
✓
$ \pm (1 - 3i)$
C
$ \pm (1 + 3i)$
D
$ \pm (3 - i)$

✓

Answer

Correct option: B.

$ \pm (1 - 3i)$

b
(b) Given that $\sqrt { - 8 - 6i} = x + iy = z$
==> $ - 8 - 6i = {(x + iy)^2}$
$\therefore {x^2} - {y^2} = - 8$ .....$(i) $ and $2xy = - 6$ .....$(ii)$
Now ${x^2} + {y^2} = \sqrt {64 + 36} = \pm 10$ .....$(iii)$
From $(i) $ and $(iii)$, we get $x = \pm 1$and $y = \pm 3$
Hence $z = \pm (1 - 3i)$
Trick : Since ${\{ \pm (1 - 3i)\} ^2} = - 8 - 6i$

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