Disc cut by the line z(1+i) + conj(z)(1-i) = c: greatest value of |z - a|^2 in the region
The same question, asked 2 times: 2021 Paper 17*, 2021 Paper 26. Every wording below, oldest first.
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Question 1
2021 Paper 17
65
Let C be the set of all complex numbers. Let S1={z∈C:∣z−2∣≤1} and S2={z∈C:z(1+i)+z(1−i)≥4}. Then, the maximum value of z−252 for z∈S1∩S2 is equal to:
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Question 2
2021 Paper 26
89
Let z be those complex number which satisfy ∣z+5∣≤4 and z(1+i)+zˉ(1−i)≥−10,i=−1. If the maximum value of ∣z+1∣2 is α+β2, then the value of (α+β) is
