[tex]\bf \textit{recall that}\qquad i^4=1\qquad i^3=-i\qquad i^2=-1\\\\
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i^{16}+i^6-2i^5+i^{13}\implies i^{4\cdot 4}~+~i^{4+2}~-~2i^{3+2}~+~i^{4+4+4+1}
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(i^4)^4~+~i^4\cdot i^2~-~2\cdot i^3\cdot i^2~+~i^4\cdot i^4\cdot i^4\cdot i^1
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(1)^4+[1\cdot -1]-[2(-i)(-1)]+[(1)(1)(1)(i)]
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1-1-2i+i\implies -i[/tex]
