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Complex Numbers question

2023 · 29 Jan · Shift 2 · Q41

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JEE Main
Mathematics
Complex Numbers
2023 · 29 Jan · Shift 2 · Q41

Complex Numbers question

2023 · 29 Jan · Shift 2 · Q41

JEE MainMathematicsComplex NumbersNumerical+4 / −1

Let

\alpha = 8 - 14i,A = \left\{ {z \in c:{{\alpha z - \overline \alpha \overline z } \over {{z^2} - {{\left( {\overline z } \right)}^2} - 112i}}=1} \right\}

and

B = \left\{ {z \in c:\left| {z + 3i} \right| = 4} \right\}

. Then

\sum\limits_{z \in A \cap B} {({\mathop{\rm Re} olimits} z - {\mathop{\rm Im} olimits} z)}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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