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Complex Numbers question

2025 · 22 Jan · Shift 1 · Q27

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JEE Main
Mathematics
Complex Numbers
2025 · 22 Jan · Shift 1 · Q27

Complex Numbers question

2025 · 22 Jan · Shift 1 · Q27

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let

z_1, z_2

and

z_3

be three complex numbers on the circle

|z|=1

with

\arg \left(z_1\right)=\frac{-\pi}{4}, \arg \left(z_2\right)=0

and

\arg \left(z_3\right)=\frac{\pi}{4}

. If

\left|z_1 \bar{z}_2+z_2 \bar{z}_3+z_3 \bar{z}_1\right|^2=\alpha+\beta \sqrt{2}, \alpha, \beta \in Z

, then the value of

\alpha^2+\beta^2

is :

A
41
B
29
C
24
D
31

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