Given, z2+z+1=0⇒z=w,w2
Now, ∣n=1∑15(zn+(−1)zn1)2∣=∣n=1∑15(z2n+z2n1+2(−1)n)∣
=∣n=1∑15w2n+w2n1+2(−1)n∣
=∣1−w2w2(1−w30)+1−w21w21(1−w301)+2(−1)∣
=∣1−w2w2(1−1)+1−w21w21(1−1)−2∣
=∣0+0−2∣=2
If z2+z+1=0,z∈C, then ∣n=1∑15(zn+(−1)azn1)2∣ is equal to _____.
Held on 26 Jun 2022 · Verified 6 Jul 2026.
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