Complex Area

Geometry Level 5

For a given sequence of real constants, \(\displaystyle \left\{\theta _i \right\}_{i=0}^n \text{, } n \in \mathbb{N} \text{ and } n \geq 2 \), the following equation holds true,

\[\displaystyle \sum_{r=0}^n z^r \cos \theta _{n-r} = 2\]

where \(z\) is a complex number.

Given that \(\displaystyle |z| < 1 \) and \(A\) denotes the minimum area in the argand plane in which the roots of the above equation lie, concluded solely by the above information, then

Evaluate : \(\displaystyle \lfloor 100A \rfloor \)


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