Let the curve z(1+i) + z(1-i) = 4, z C, divide the region |z-3| ≤ 1 into two parts of areas α and β. Then |α - β| equals:

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q44

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

Let the curve

z(1+i) + \bar{z}(1-i) = 4, z \in \mathbb{C}

, divide the region

|z-3| \leq 1

into two parts of areas

\alpha

and

\beta

. Then

|\alpha - \beta|

equals: