I have no idea why people ignore Argand diagrams and Euler's formula: e^(iθ) = cosθ + i sinθ x¹²=1=e^(i2πn) for n=0,1,2,3,... 11 (repeats thereafter) x=e^(iπn/6) giving four roots on the (Argand diagram) axes (1,-1,i,-i) and two sets of four roots based on 30,60,90 triangles : ±√3/2±i/2 and ±1/2±i√3/2
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Much simpler in polar coordinates. r, theta
I have no idea why people ignore Argand diagrams and Euler's formula: e^(iθ) = cosθ + i sinθ
x¹²=1=e^(i2πn) for n=0,1,2,3,... 11 (repeats thereafter)
x=e^(iπn/6)
giving four roots on the (Argand diagram) axes (1,-1,i,-i) and
two sets of four roots based on 30,60,90 triangles : ±√3/2±i/2 and ±1/2±i√3/2