Question

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

• A. 1$\pm$3i
• B. $\pm$(1-3i)
• C. $\pm$(1+3i)
• D. $\pm$(3-i)

Answer 1

The correct option is B

$\pm$(1-3i)

Given that $\sqrt{-8-6i}$=x+iy=z

$\Rightarrow$ -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 (ii),we get x=$\pm$1 and y=$\pm$3

Hence z=$\pm$(1-3i)

Trick: Since{$\pm$$(1-3i{)}^2$} = -8-6i