Complication Transformation

Geometry Level 3

Let α \alpha and β \beta denote complex numbers such that ∣ α − 1 ∣ = 1 |\alpha - 1| = 1 and ∣ β − i ∣ = 1 |\beta - i| = 1 . Which of the following best illustrates the region ( α − 1 ) ( β − 1 ) (\alpha - 1)(\beta - 1) in the Argand plane ?

Circular annulus Complete circle Elliptic annulus Complete ellipse None of the given choices above.

Michael Huang by Michael Huang , 29, USA

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1 solution

Jason Gomez
Feb 6, 2021

4 Helpful 3 Interesting 4 Brilliant 0 Confused

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