Mathematics: What is i^16 - i^15 + 1^14 - 1^13? i think its zero, but if you could get back to me with the answers and how you got it that would be great : )

What is i^16 - i^15 + 1^14 - 1^13? i think its - id16151141131345204, LuluMathLover101

Ответ:

Arealbot

14.03.2022

$\bf \stackrel{\stackrel{i^{4+4+4+4}}{i^4i^4i^4i^4}}{i^{16}}-\stackrel{\stackrel{i^{2+3}}{i^2i^3} }{i^5}+\stackrel{\stackrel{i^{4+4+4+2}}{i^4i^4i^4i^2}}{i^{14}}-\stackrel{\stackrel{i^{4+4+4+1}}{i^4i^4i^4i}}{i^{13}}
\\\\\\
(1\cdot 1\cdot 1\cdot 1)-(-1\cdot i)+(1\cdot 1\cdot 1\cdot -1)-(1\cdot 1\cdot 1\cdot i)
\\\\\\
1+i-1-i\implies 0$