Hey guys, I've done more questions that I need to check.

1) a) Simplify (z-1) (z^4 + z^3 + z^2 + z + 1)

my solution: z^5 -1

b) use part a to find all the roots of the polynomial P(z) = z^4 + z^3 + z^2 + z + 1 (you may keep your answer in exponential polar form

my solution: I converted z^5 - 1 = 0 to exponential polar form and got the following roots: z = 1e^i0, 1e^i(2pi/5), 1e^i(-2pi/5), 1e^i(4pi/5), 1e^i(-4pi/5)

2) Find dy/dx if root(y) + x loge(y) = cos(xy^2)

my solution: using implicit diff and multiplication rule, i got dy/dx = [-log(y) - y^2 sin(xy^2)] / [ (x^2/2y) + 2x sin(xy^2) + (x^2/y)]

please check my solutions to these problems

thank you in advance.