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Let z=(-1+sqrt(3)i)/(2), where i=sqrt(-1...

Let `z=(-1+sqrt(3)i)/(2)`, where `i=sqrt(-1)`, and `r, s in {1, 2, 3}`. Let `P=[((-z)^(r),z^(2s)),(z^(2s),z^(r))]` and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which `P^(2)=-I` is ______.

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VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. about to only mathematics

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  2. about to only mathematics

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