Let z be a complex number such that |z|=1. If (2 + k² z)/(k + z) = k z, k, then the maximum distance of k + i k² from the circle |z - (1 + 2i)| = 1 is:

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q35

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let

z

be a complex number such that

|z|=1

. If

\displaystyle\frac{2 + k^2 z}{k + \overline{z}} = k z

k\in\mathbb{R}

, then the maximum distance of

k + i k^2

from the circle

|z - (1 + 2i)| = 1

is: