Question

Solve:

$\sqrt{8-6i}=$

• A. $3-4i$
• B. $3-2i$
• C. $3-i$
• D. $3+4i$

Answer 1

The correct option is C $3-i$

$\sqrt{8-6i}=x=(a+ib)$
$\therefore x^2=8-6i$
$\therefore (a+ib{)}^2=8-6i$
$\therefore$ comparing real & imaginary parts
$a^2-b^2=8$--------------------------------------(1)
$2ab=-6$-------------------------------------(2)
$as\left|x^2\right|={|8-6i|}^2$
$\therefore a^2+b^2=\sqrt{8^2+6^2}=10$--------------------------------(3)
solving (1)$\&$(3),

$a^2=9$ &

$b^2=1$

Hence,
$a=\pm 3$ & $b=\pm 1$

From (2)
$a$ & $b$ are of opposite signs
$a=3,b=-1$ or

$a=-3orb=1$
$\therefore x=\pm (3-i)$