Use your answers from part (c) to factor the polynomial P (z) into threequadratics with real coefficients. (You may use the facts that cos( π12 ) = √6+√24 andsin( π12 ) = √6−√24 ).Before you submit this work, make sure to check your answer. If you multiply outyour quadratic factors, you should recover P (z).3

Let z = −2√3 + 6ia) Express z|z| in polar form.b) Determine z4
8 in polar form, in terms of its principal argument.c) Determine all distinct values of z1/4 in polar form, in terms of their principal argument.

n this question, we will use techniques involving complex numbers to study the sexticpolynomial defined byP (z) = z6 − 4z3 + 8.(a) (1 mark) Use the quadratic formula to find the set of possible values of z3 such thatP (z) = 0. (Note that we are not trying to find the values of z yet - only the values ofz3.)(b) (2 marks) In the WebWork part of this assignment, you found the three solutions ofz3 = 2 − 2i in exponential polar form.Use a similar method to find the three solutions of z3 = 2 + 2i. Express your answerin exponential polar form.2(c) (1 mark) Use the results of the previous parts to find the six values of z such thatP (z) = 0. Express your answers in exponential polar form.(d) (3 marks) Use your answers from part (c) to factor the polynomial P (z) into threequadratics with real coefficients. (You may use the facts that cos( π12 ) = √6+√24 andsin( π12 ) = √6−√24 ).Before you submit this work, make sure to check your answer. If you multiply outyour quadratic factors, you should recover P (z).

6z 2 −24z+16=−3z 2

It is given that z1 = 3 cis(3π__4 ) and z2 = 2 cis(nπ__16) , n∈ ℤ+ .(a) In parts (a)(i) and (a)(ii), give your answers in the form r eiθ , r ≥ 0 , − π < θ ≤ π .(i) Find the value of z13

actor the polynomial completely. Do NOT put any spaces in your answers.Must show work/steps on your work page𝑥2−4𝑥+3 =