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Complex Numbers question

2024 · 1 Feb · Shift 1 · Q57

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JEE Main
Mathematics
Complex Numbers
2024 · 1 Feb · Shift 1 · Q57

Complex Numbers question

2024 · 1 Feb · Shift 1 · Q57

JEE MainMathematicsComplex NumbersNumerical+4 / −1

Let

\mathrm{P}=\{\mathrm{z} \in \mathbb{C}:|z+2-3 i| \leq 1\}

and

\mathrm{Q}=\{\mathrm{z} \in \mathbb{C}: z(1+i)+\bar{z}(1-i) \leq-8\}

. Let in

\mathrm{P} \cap \mathrm{Q}

,

|z-3+2 i|

be maximum and minimum at

z_1

and

z_2

respectively. If

\left|z_1\right|^2+2\left|z_2\right|^2=\alpha+\beta \sqrt{2}

, where

\alpha, \beta

are integers, then

\alpha+\beta

equals

\underline{\hspace{2cm}}

.

Numerical answer

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