Question

Find square root of $a^2-1+2a\sqrt{-1}$.

• A. $\pm (a+2i).$
• B. $\pm (a-i).$
• C. $\pm (a+i).$
• D. $\pm (a+1).$

Answer 1

The correct option is C $\pm (a+i).$

1st Method. $a^2-1+i.2a$Half the conefficient of i is a or a. 1.
Its factors are a, 1 such that $a^2-1=R.P.$
$\therefore$ Square root is $\pm (a+i).$
Alt. $a^2-1+2a\sqrt{-1}=a^2+i^2+2ai={(a+i)}^2$
Hence $\sqrt{(a^2-1)+2a\sqrt{-1}}=\pm (a+i).$
Ans: C