The infinite plot with a finite area

Algebra Level 4

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

{a2+b2(a+b)2a2+b21.\begin{cases} a^2 + b^2 \geq (a + b)^2\\ a^2 + b^2 \leq 1. \end{cases}

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

Details and Assumptions

  • ee is the base of the natural logarithm.

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


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