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Question Number 126267 by mathocean1 last updated on 19/Dec/20
z≠0 and z is complex; z=x+iy with x;y ∈ R^∗ . Given these points with theirs affix: 0(0+0i); N(z^2 −1) and P((1/z^2 )−1) 1. Show that ((1/z^2 )−1)z^2 −1^(−) =−z^2 ^(−) ∣(1/2)−1∣^2 . 2. What is the nature of the set of points M(z) such that O, N and P are aligned?
z≠0andziscomplex;z=x+iywithx;y∈R∗.Giventhesepointswiththeirsaffix:0(0+0i);N(z2−1)andP(1z2−1)1.Showthat(1z2−1)z2−1―=−z2―∣12−1∣2.2.WhatisthenatureofthesetofpointsM(z)suchthatO,NandParealigned?

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