Question

Which simplifications of the powers of i are correct? There may be more than one correct answer.

Select all correct answers.
I^22=1
I^11=−i
I^21=i
I^12=i
I^20=1
I^26=−1
I^27=i

Answer 1

`\bf i^2=-1\qquad\qquad i^3=-i\qquad \qquad i^4=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ i^(22)\implies i^((4\cdot 5)+2)\implies i^(4\cdot 5)i^2\implies (i^4)^5 i^2\implies 1^5(-1)\implies -1~\dotfill \bigotimes \\\\\\ i^(11)\implies i^((2\cdot 5)+1)\implies (i^2)^5 i\implies (-1)^5(i)\implies -i~\dotfill \checkmark`

`\bf i^(21)\implies i^((4\cdot 5)+1)\implies (i^4)^5 i\implies 1^5(i)\implies i~\dotfill \checkmark \\\\\\ i^(12)\implies i^(3\cdot 4)\implies i^3 i^4\implies (-i)(1)\implies -i\dotfill \bigotimes \\\\\\ i^(20)\implies i^(4\cdot 5)\implies (i^4)^5\implies 1~\dotfill \checkmark \\\\\\ i^(26)\implies i^((4\cdot 6)+2)\implies (i^4)^6 i^2\implies 1^6(-1)\implies -1\dotfill \checkmark \\\\\\ i^(27)\implies i^((4\cdot 6)+3)\implies (i^4)^6 i^3 \implies 1^6(-i)\implies -i\dotfill \bigotimes`