Is it possible to take the square root of a negative number? If so, how do you show it?

Answer 1

Make it a positive number, take the square root, and put an "i" in front of it.

This is because Sqrt(-1) = i, and any negative number can be written as n*(-1).

Answer 2

yes that would be imaginary numbers i
/-1=i
so /-4=/-1*/2=2i

Answer 3

Yes. Use Euler's relationship:

i = e^(i*pi/2)

then:

sqrt(i) = sqrt(e^(i*pi/2)) = exp(i*pi/4) = cos(pi/4) +i*sin(pi/4)
= 0.707 + i*0.707