Let D be the interior of the closed contour formed by C = the left half...

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Let D be the interior of the closed contour formed by C₁ = the left half of the unit circle {e¹/2 ≤ 03/2} and C2 = the line segment between-i and i. a) Find a Fractional Linear Transofrmation f(z) such that f(i) = 0 and_lim f(z) = = ∞. There are many correct answers. b) f(D) will be the region between two rays reo and red through the origin. Identify 0o and 01. c) By composing an anlaytic branch of log and f, and manipulating the imaginary part of the composition, describe a harmonic function on D with limit 1 on C₁ and 2 on C₂. No need for an explicit formula. Let D be the interior of the closed contour formed by C₁ = the left half of the unit circle {e¹/2 ≤ 03/2} and C2 = the line segment between-i and i. a) Find a Fractional Linear Transofrmation f(z) such that f(i) = 0 and_lim f(z) = = ∞. There are many correct answers. b) f(D) will be the region between two rays reo and red through the origin. Identify 0o and 01. c) By composing an anlaytic branch of log and f, and manipulating the imaginary part of the composition, describe a harmonic function on D with limit 1 on C₁ and 2 on C₂. No need for an explicit formula.