`sqrt(-i)` का मान (जहाँ, `i = sqrt(-1))` किसके बराबर हैं?

Options

A. `+-((1-i)/(sqrt(2)))`
B. `+-((1+i)/(sqrt(2)))`
C. `+-((1-i)/(2))`
D. `+-((1+i)/(2))`

Answer

A

Explanation

`because sqrt(-i) = sqrt(e^(-ipi//2)) " " [because e^(itheta) = "cos" theta + "i sin" theta]`
` = +- e^(-i(pi)/(2) * (1)/(2))`
` = +-e^(-i(pi)/(4)) = +- ["cos" ((pi)/(4)) - "i sin" ((pi)/(4))]`
` = +- ((1-i)/(sqrt(2)))`