Let w = r e^alpha i be any nonzero complex number. then w has n nth roots: n solutions to the equation z^n = r e^i alpha or r^n e^intheta = r e^i alpha which have r = r^1/n and theta = alpha/n + 2pik/n. the nth roots of w are w^1/n = z = r^1/n ei(alpha/n + 2pik/n), where k = 0, 1, 2, n-1. the n nth roots of w are equispaced on the circle c of radius r^1/n centered at the origin. draw the circle c, and then find the three 3rd roots of i. the circle c has radius the angle difference (in radians) between adjacent 3th roots is draw the circle c, and then find the four 4th roots of -16. the circle c has radius the angle difference (in radians) between adjacent 4th roots is draw the circle c, and then find the two square roots (2nd roots! ) of 1 + i. the circle c has radius . the angle difference (in radians) between adjacent square roots is .

Consider the following geometry problems in 3-space enter t or f depending on whether the statement is true or false. (you must enter t or f -- true and false will not work.) f equation editorequation editor 1. a plane and a line either intersect or are parallel t equation editorequation editor 2. two planes parallel to a third plane are parallel f equation editorequation editor 3. two lines either intersect or are parallel f equation editorequation editor 4. two planes orthogonal to a third plane are parallel f equation editorequation editor 5. two planes orthogonal to a line are parallel f equation editorequation editor 6. two planes either intersect or are parallel f equation editorequation editor 7. two lines orthogonal to a third line are parallel t equation editorequation editor 8. two lines parallel to a third line are parallel t equation editorequation editor 9. two planes parallel to a line are parallel f equation editorequation editor 10. two lines parallel to a plane are parallel f equation editorequation editor 11. two lines orthogonal to a plane are parallel