I have a whole load of questions that I have attempted but could not do. Hopefully someone here can help me out!
1. Express z^4 + z^3 + z^2 + z + 1 as a product of two real quadratic factors.
2. Find the zeros of z^5 - 1, giving your answers in the form r(cos theta + i sin theta), where r > 0 and -pi < theta < pi.
3. Z1 and Z2 are complex numbers on the Argand diagram relative to the origin. If |Z1 + Z2| = |Z1 - Z2| where | | denotes the moduli, show that arg Z1 and arg Z2 differ by pi/2
If you can do any of these, that would be great. I've been stuck on these for a while now.