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Given-a-transformation-T-C-C-z-Show-that-if-z-i-z-1-then-z-i-1-Hence-the-image-of-the-line-z-i-z-2-under-the-transformation-T-the-plane-is-a-circle-w

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Question Number 110504 by Rio Michael last updated on 29/Aug/20
Given a transformation , T: C → C ; z → ω Show that if ω = ((z−i)/(z +1)) then z = ((ω + i)/(1−ω)). Hence the image of the line ∣z−i∣ = ∣z + 2∣ under the transformation T the ω−plane is a circle with center (−2,−i) and radius (√(10)) .
Givenatransformation,T:C→C;z→ωShowthatifω=z−iz+1thenz=ω+i1−ω.Hencetheimageoftheline∣z−i∣=∣z+2∣underthetransformationTtheω−planeisacirclewithcenter(−2,−i)andradius10.

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