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Complex Numbers question

2023 · 13 Apr · Shift 1 · Q39

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JEE Main
Mathematics
Complex Numbers
2023 · 13 Apr · Shift 1 · Q39

Complex Numbers question

2023 · 13 Apr · Shift 1 · Q39

JEE MainMathematicsComplex NumbersNumerical+4 / −1

Let

w=z \bar{z}+k_{1} z+k_{2} i z+\lambda(1+i), k_{1}, k_{2} \in \mathbb{R}

. Let

\operatorname{Re}(w)=0

be the circle

\mathrm{C}

of radius 1 in the first quadrant touching the line

y=1

and the

y

-axis. If the curve

\operatorname{Im}(w)=0

intersects

\mathrm{C}

at

\mathrm{A}

and

\mathrm{B}

, then

30(A B)^{2}

is equal to

\underline{\hspace{2cm}}

Numerical answer

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