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Complex Numbers question

2023 · 12 Apr · Shift 1 · Q28

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JEE Main
Mathematics
Complex Numbers
2023 · 12 Apr · Shift 1 · Q28

Complex Numbers question

2023 · 12 Apr · Shift 1 · Q28

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let

\mathrm{C}

be the circle in the complex plane with centre

\mathrm{z}_{0}=\frac{1}{2}(1+3 i)

and radius

r=1

. Let

\mathrm{z}_{1}=1+\mathrm{i}

and the complex number

z_{2}

be outside the circle

C

such that

\left|z_{1}-z_{0}\right|\left|z_{2}-z_{0}\right|=1

. If

z_{0}, z_{1}

and

z_{2}

are collinear, then the smaller value of

\left|z_{2}\right|^{2}

is equal to :

A
$\frac{3}{2}$
B
$\frac{5}{2}$
C
$\frac{13}{2}$
D
$\frac{7}{2}$

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