Only c and d ( c and d )Last 2 parts asap plz handwritten solution acceptableNeed urgentlyWill definitely upvote 2. Let be a real number such that 0 < 0 < 2π. Let n be a positive integer.(a) Show that for each complex number z ‡ 1,(b) Show that(c) Show thatnk=0=zkTrett=1 — zn+11-znΣ cos(k0) = Re (Σ (et)k=0n= Re (Σ (e²9) *).k=0nΣ (eio) kk=0Hint: Factor e¹0/2 out of the numerator and denominator on the left-hand side.(d) Use parts (b) and (c) to show that1- ei(n+1)01- eieei(2n+1)0/2e-i0/22i sin (0/2)1 + cos(0) + cos(20) + ... + cos(ne)1= +2sin((2n + 1)0/2)2 sin(0/2)

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(a) Show that for each complex number z ‡ 1, (b) Show that (c) Show that η n Στ k=0 Text Σcos(k0) k=0 = – 1-₂n+1 1-z n Re (Σ (et) k=0 (eroja). n Σ (eig)* k=0 Hint: Factor eit/2 out of the numerator and denominator on the left-hand side. (d) Use parts (b) and (c) to show that 1 – pi(n+1)θ 1 ρίθ ei(2n+1)0/2 –10/2 e 2i sin(θ/2) 1 + cos(0) + cos(20) + ... + cos(nθ) 1 = + 2 sin((2n + 1)0/2) 2 sin(θ/2)