Question

Square roots of - 7 - 24i are :

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$Letz=-7-24i=(a-ib{)}^2\Rightarrow a^2-b^2=-7,2iab=-24i\Rightarrow a^2-b^2=-7,ab==-12\Rightarrow (a^2+b^2{)}^2=49+576=625\Rightarrow a^2-b^2=-7,a^2+b^2=25\Rightarrow a^2=9,b^2=16\Rightarrow a=3,b=-4ora=-3,b=4\text{Hence}\sqrt{-7-24i}=\underset{-}{+}(3-4i)Aliter:Here|z|=25,b=-24<0\therefore \sqrt{z}=\sqrt{\frac{25-7}{2}}-i\sqrt{\frac{25+7}{2}}=\underset{-}{+}(3-4i)$