Think A Little Bit

Geometry Level 4

Let nN\forall n \in \mathbb{N}, zn+1=4zn(1zn)z_{n+1}=4z_n(1-z_n) where z1=358z_1=\frac{3-\sqrt{5}}{8}.

Find z5×z10z_5 \times z_{10}.

If answer can be expressed in form a/ba/b, where aa and bb are coprime positive integers, find a+ba+b .

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