Question

Use the identity i2 = -1 to compute the powers of i and complete the table.

i3-

i4-

i5-

i6-

i7-

i4n-

i4n+1-

i4n+2-

i4n+3-

Answer 1

hint:
`\bf \begin{array}{llll} i^(3)\to & i^2\cdot i^1\\\\ i^(4)\to & i^2\cdot i^2\\\\ i^(5)\to & i^2\cdot i^2\cdot i^1\\\\ i^(6)\to & i^2\cdot i^2\cdot i^2\\\\ i^(7)\to & i^2\cdot i^2\cdot i^2\cdot i^1\\\\ i^(4n)\to & (i^(4))^n\\\\ i^(4n+1)\to & (i^4)^n\cdot i^1\\\\ i^(4n+2)\to & (i^4)^n\cdot i^2\\\\ i^(4n+3)\to & (i^4)^n\cdot i^3 \end{array}`