# The infinite plot with a finite area

Algebra Level 4

Let $x$ be the sum of the areas formed when plotting the given equations:

$\begin{cases} a^2 + b^2 \geq (a + b)^2\\ a^2 + b^2 \leq 1. \end{cases}$

Find the value of $(e^{ix})^2.$

Details and Assumptions

• $e$ is the base of the natural logarithm.

• $i$ is the imaginary unit $i=\sqrt {-1}.$

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