Mathematics · Complex Analysis
Let T be the Möbius transformation that maps the points 0, 12 and 1 conformally onto the points -3, ∞ and 2, respectively, in the extended complex plane. If T maps the circle centred at 1 with radius k onto a straight line given by the equation αx + βy + γ = 0, then the value of 2k(α + β) + γα + β - 2kγ is equal to:
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