If root(x+iy) = plus or minus(a+ib), then root(-x-iy) is equal to

Solution:

Given √(x+iy) = ±(a+ib)

Squaring both sides

(x+iy) = (a+ib)²

= a²+2aib-b²

= a²-b²+2aib

Comparing real and imaginary part

x = a²-b²

y = 2ab

-x-iy = -a²+b²-i2ab

= (-b+ia)²

Taking square root

√(-x-iy) = ±(-b+ia)

Hence option (5) is the answer.

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