root12.html

> solve(x^12+1=0,x);

$- \frac{1}{2} \sqrt{2} + \frac{1}{2} ⅈ \sqrt{2}, \frac{1}{2} \sqrt{2} - \frac{1}{2} ⅈ \sqrt{2}, - \frac{1}{2} \sqrt{2} - \frac{1}{2} ⅈ \sqrt{2}, \frac{1}{2} \sqrt{2} + \frac{1}{2} ⅈ \sqrt{2}, - \frac{1}{2} \sqrt{- 2 \sqrt{(2 + 2 ⅈ \sqrt{3})}}, \frac{1}{2} \sqrt{- 2 \sqrt{(2 + 2 ⅈ \sqrt{3})}}, - \frac{1}{2} \sqrt{2} \sqrt[4]{(2 + 2 ⅈ \sqrt{3})}, \frac{1}{2} \sqrt{2} \sqrt[4]{(2 + 2 ⅈ \sqrt{3})}, - \frac{1}{2} \sqrt{- 2 \sqrt{(2 - 2 ⅈ \sqrt{3})}}, \frac{1}{2} \sqrt{- 2 \sqrt{(2 - 2 ⅈ \sqrt{3})}}, - \frac{1}{2} \sqrt{2} \sqrt[4]{(2 - 2 ⅈ \sqrt{3})}, \frac{1}{2} \sqrt{2} \sqrt[4]{(2 - 2 ⅈ \sqrt{3})}$

> z(x,y):=abs((x+y*I)^12+1);

$z (x, y) := &LeftBracketingBar;{(x + ⅈ y)}^{12} + 1&RightBracketingBar;$

> plot3d(z(x,y),x=-1..1,y=-1..1, axes=boxed,view=[-1..1,-1..1,0..1],numpoints=2048);

> plot3d(z(x,y),x=-1..1,y=-1..1, axes=boxed,numpoints=2048);