Question

If $\sqrt{x+iy}=\pm (a+ib),$ then $\sqrt{-x-iy}$ is equal to

• A. $\pm (b+ia)$
• B. $\pm (a-ib)$
• C. $(ai+b)$
• D. $\pm (b-ia)$

Answer 1

Answer: (D)

$\pm (b-ia)$

Answer 2

Given, $\sqrt{x+iy}=\pm (a+bi)$
$\Rightarrow$ $x+iy={{a}^{2}}-{{b}^{2}}+2iab$
$\Rightarrow$ $x={{a}^{2}}-{{b}^{2}},y=2ab$
$\therefore \,\,\,\,\sqrt{-x-iy}=\,\sqrt{-({{a}^{2}}-{{b}^{2}})-2\,iab}$
$=\sqrt{{{b}^{2}}-{{a}^{2}}-2iab}\,=\sqrt{{{(b-ia)}^{2}}}$
$=\pm \,(b-ia)$