Please help me write the steps in detail! Thank you!

[10 points total] Consider the polynomial Z4 1. We will solve some problems surrounding this polynomial. Part (a) [2 points] What are the roots of this polynomial? Give them in both the form 2 = a + bi (cartesian form) and |z|ei9 (polar form). Recall that 6'59 = cos(9) + sin(6), and [2| = Vaz + b2 Part (b) [3 points] Consider the vector space P4, the vector space of poly nomials of at most degree four, with scalars over the real numbers. Let R = {T1,r2, r3,r4} be the set of 4 roots to Z4 1 found above. Choose both of the imaginary roots n1 , rig, and show that 'V=@WHPWJ=0mMn=W is a subspace of P2 Part (c) [3 points] Find a basis for this subspace V Hint: you already have two polynomials with both as a root (if you factored into two quadratics, if not give it a try). To show these span, take a polynomial (1534 + 51333 + 6932 + dx + e, and consider what equations you get on a, b, c, d when substituting our imaginary roots ml and r152. Linear independence is easier. Part ((1) [2 points] Now take the two real roots n1 , Trz V=@@HPWJ=OMMWJ=M Show that this is not a subspace