Let the complex numbers α and 1/(α) lie on the circles |z-z₀|²=4 and |z-z₀|²=16 respectively, where z₀=1+i. Then, the value of 100|α|² is _ _ _ _ _.

Complex Numbers and Quadratic Equations: JEE Main 2024 Mathematics question

JEE Main 2024 · 27 Jan, Evening shift · Q29

JEE Main 202427 Jan, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let the complex numbers

\alpha

and

\frac{1}{\bar{\alpha}}

lie on the circles

\left|z-z_0\right|^2=4

and

\left|z-z_0\right|^2=16

respectively, where

z_0=1+i

. Then, the value of

100|\alpha|^2

is __________.

Your answerType your answer. Integers and decimals are accepted.