Question

Să se calculeze
$(1 - i) \times (1 - {i}^{2} ) \times (1 - {i}^{3} ) \times ... \times (1 - {i}^{2009} )$
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Answer 1

$(1-i)(1-i^2)(1-i^3)(1-i^4)(1-i^5)\cdot...\cdot (1-i^{2009})=\\ \\ = (1-i)(1+1)(1+i)\cdot (1-1)\cdot (1-i)\cdot...\cdot (1-i^{2009}) \\ \\ =(1-i)(1+1)(1+i)\cdot 0\cdot (1-i)\cdot ...\cdot (1-i^{2009})\\ \\ = \boxed{0}$