Question

What is i^16 - i^15 + 1^14 - 1^13?

Answer 1

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