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Complex Numbers question

2023 · 11 Apr · Shift 2 · Q41
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  5. /2023 · 11 Apr · Shift 2 · Q41

Complex Numbers question

2023 · 11 Apr · Shift 2 · Q41

JEE MainMathematicsComplex NumbersNumerical+4 / −1
Let S={z∈C−{i,2i}:z2+8iz−15z2−3iz−2∈R}\mathrm{S}=\left\{z \in \mathbb{C}-\{i, 2 i\}: \frac{z^{2}+8 i z-15}{z^{2}-3 i z-2} \in \mathbb{R}\right\}S={z∈C−{i,2i}:z2−3iz−2z2+8iz−15​∈R}. If α−1311i∈S,α∈R−{0}\alpha-\frac{13}{11} i \in \mathrm{S}, \alpha \in \mathbb{R}-\{0\}α−1113​i∈S,α∈R−{0}, then 242α2242 \alpha^{2}242α2 is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
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