27.10.25.md (1000B)
1 27/10/25 2 ======== 3 4 - see FIG1 for a use of eulers formula, when adding angles in polar form 5 - we can use De moivres formula to multiply angles 6 7 - the roots of unity all lie on the unit circle (with an imaginary y axis) 8 - each root is evenly distributed along the unit circle 9 - see fig4 for the roots of unity formula 10 - n is the number of roots that you are looking for 11 - when n is 0, the root is always 1, meaning 1 is always a root 12 - FIG3 shows how to find the 5th root of unity 13 - m must be substituted in for all its values 14 15 - to solve complex roots (see FIG4 for a worked example) 16 - write the right hand side in polar form 17 - multiply the right hand side by e^(2 PI i m) where m is an int 18 - take the nth root of the right hand side 19 - convert back into polar form (magnitude and angle) 20 - substitued the values of m into the angle 21 - we can then draw this on a circle, it will have a radius of the magnitude 22 - then draw on the angles found before 23 24