Just got back from a 5 day deca competion so I forgot the easiest shit lol

Find square roots of: -25i

Cube roots of: -125/2 (1+ i square root of 3)

You need to write out your problems in correct notation.

There is no such thing as sqrt(-25i)

Maybe you want to solve the following equations :

X ² = - 25.i

X^3 = - 125/2 (1+ i √ 3)

In both cases, use the exponential form :

- 25.i = 25.exp ( -i.pi / 2 )

- 125/2 (1+ i √ 3) = 125.exp ( -i.pi / 3 )

Find the solutions by taking the square-root (or the cube-root) of the magnitude (it's easy with your values), and divide by 2 (or 3) the argument - don't forget to add pi or 2pi/3, 4pi/3 to find all the solutions.

Good luck !

since when?

sqrt(-25i) = sqrt(-1) * sqrt(25) * sqrt(i) = [taking the positive roots] = i * 5 * (0.707106781 + 0.707106781*i)

btw, 0.707106781 ~ 1/sqrt(2)

just square [1/sqrt(2)]*(1+i) and you will see that you get i