Find all complex cube roots of i.?

(-i)³ = (-1)³ × i² × i = -1 × -1 i = i

(±½√3 + ½i)³ = ⅛(±3√3 + 3×3i ∓ 3√3 - i) = ⅛(9i - i) = i

So the complex cube roots of i are -i, -½√3 + ½i and ½√3 + ½i

Graph: https://www.desmos.com/calculator/7kaczy2xys

X= -¡

X=1/2 ({root of 3} + ¡)

X= 1/2 ({negative root of 3} + ¡)

i = cis 90

The arguments of the cube roots are (90 + 360n)/3, for n = 0, 1, and 2.

cube roots are cis 30, cis 150 and cis 270

I'll leave it to you to convert cos30, sin30 etc to actual numbers.