Part BCSIR NET December 2024one-interior-point-fixes-which-side-maps-in

One interior point fixes which side maps in

Consider the half planes R₊ = {z = x + iy $\in C : x > 0$ } and R₋ = {z = x + iy $\in C : x < 0$ }, and the fractional linear transformations $T_{1} (z) = (z - 1) / (z + 1)$ and $T_{2} (z) = (z + 1) / (z - 1)$ . Let disc 𝔻 = { $z \in C$ : |z| < 1}. Which of the following statements is true?

A. $T_{1}$ and $T_{2}$ conformally map R₊ and R₋ respectively, onto the disc 𝔻✓
B. $T_{1}$ and $T_{2}$ conformally map R₋ and R₊ respectively, onto the disc 𝔻
C. $T_{1}$ and $T_{2}$ conformally map the disc 𝔻 onto, respectively R₊ and R₋
D. $T_{1}$ and $T_{2}$ conformally map the disc 𝔻 onto, respectively R₋ and R₊

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

One interior point fixes which side maps in

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