вычислить значение выражения i^11-i^34+i^49-i^16. Created by AltMarsh. matematika-ru

вычислить значение выражения i^11-i^34+i^49-i^16...

AltMarsh @AltMarsh

August 2022 1 7 Report

вычислить значение выражения i^11-i^34+i^49-i^16

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$i^{11}=i^{10}\cdot i=(1^2)^5\cdot i=(-1)^5\cdot i=-i\\\\i^{34}=(i^2)^{17}=(-1)^{17}=-1\\\\i^{49}=i^{48}\cdot i=(i^2)^{24}\cdot i=(-1)^{24}\cdot i=+1\cdot i=i\\\\i^{16}=(i^2)^8=(-1)^8=+1\\\\\\i^{11}-i^{34}+i^{49}-i^{16}=-i-(-1)+i-1=-i+1+i-1=0$

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