A-Level Further Maths B10-03 Complex Numbers: Solve z^6=1

[RanDom-iudb]

If anyone is wondering how someone in AS FM would answer the question z^6=1;
first -1 on both side: z^6-1=0
second use difference of two squares: (z^3+1)(z^3-1)=0
consider each in turn ill be choosing: z^3+1=0
we know z=-1 is a solution to z^3+1=0, therefore (z+1) is a linear factor of z^3+1=0
multiply this factor by some quadratic function: (z+1)(az^2+bz+c) == z^3 + 1
consider constants c=1, consider z^3 term a=1 and consider z coefficients c+b=0 implies 1+b=0 therefore b = -1
(z+1)(z^2-z+1)=0 and solve the first quadratic
repeat the step for the other bracket: z^3-1=0 and then you should have all the solution, we know z=1 is a solution for this one.
hope this helps for AS Edexcel since this was a challenge question on AS Core pure 1

[THE-MOES-SHOW]

I'm really enjoying these! Even though i'm not taking further maths and let alone started my As level maths studies. I'm Looking forward to year 12 Thanks for the videos they will be very helpful :D

[detsolinaa]

Great videos man, clear and straight to the point. They really helped me a lot.