Let C be the circle in the complex plane with centre z₀=1/2(1+3 i) and radius r=1. Let z₁=1+i and the complex number z₂ be outside the circle C such that |z₁-z₀||z₂-z₀|=1. If z₀, z₁ and z₂ are collinear, then the smaller value of |z₂|² is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 12 Apr, Morning shift · Q3200

JEE Main 202312 Apr, Morning shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

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 :