Let S = z C: |z - 3| ≤ 1 and z(4 + 3i) + z (4 - 3i) ≤ 24. If α + i β is the point in S which is closest to 4i, then 25(α + β) is equal to _ _ _ _ _ _.

Complex Numbers and Quadratic Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 24 Jun, Evening shift · Q33

JEE Main 202224 Jun, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let S = {z

\in

C : |z

-

\le

1 and z(4 + 3i) +

\overline z

-

3i)

\le

24}. If

\alpha

+ i

\beta

is the point in S which is closest to 4i, then 25(

\alpha

\beta

) is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.