If are the th roots of unity

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

If z1,z2,z3,…,znz_1,z_2,z_3,\dots,z_n are the nnth roots of unity, then for k=1,2,3,…,nk=1,2,3,\dots,n, (1) ∣zk∣=k∣zk+1∣|z_k|=k|z_{k+1}| (2) ∣zk+1∣=k∣zk∣|z_{k+1}|=k|z_k| (3) ∣zk+1∣=∣zk∣+∣zk−1∣|z_{k+1}|=|z_k|+|z_{k-1}| (4) ∣zk∣=∣zk+1∣|z_k|=|z_{k+1}|

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