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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