F92+590+ 588586584582 + 580+ 578+576+ 574 – InterviewSolution

1.

F92+590+ 588586584582 + 580+ 578+576+ 574

Answer»

i^574(i^18+ i^16+ i^14+i^12+ i^10+ i^8+ i^6+ i^4+ i^2+ 1 )

= (i^2)^287 ( (i^2)^9+(i^2)^8+(i^2)^7+(i^2)^6+(i^2)^5+(i^2)^4+(i^2)^3+(i^2)^2+(i^2)^1+ 1)

= -1 ( -1 + 1-1 +1 -1+1-1+1-1+1)

= 0

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