Question

Help me pleasssseeeeeee

Answer 1

`i^(46) = -i`

~~~~~~~~~~~~~~~~~~~

46/4 = 11 remainder 2 =
`-i`

47/4 = 11 remainder 3 = 1

48/4 = 11 remainder 0 =
`i`

49/4 = 11 remainder 1 = -1

Explanation:

`i = √(-1) = i` (remainder 0)

`i^(2) = √(-1) * √(-1) = -1` (remainder 1)

`i^(3) = √(-1) * √(-1) * √(-1)= -1 * √(-1) = -i` (remainder 2)

`i^(4) = √(-1) * √(-1) * √(-1) * √(-1)= -1 * -1 = 1\\` (remainder 3)

`i^(5) = √(-1) * √(-1) * √(-1) * √(-1)* √(-1)= 1 * √(-1) = i\\` (remainder 0)

The pattern repeats every FOUR in the exponent

Answer 2

`{ \bf{b. \: \: {i}^(47) }}`

Explanation:

`{i}^(46) = ( {i}^(2) ) {}^(23) = - 1 \\ \\ {i}^(47) = (i)( {i}^(46) ) = ( - 1 * i) = - i \\ \\ {i}^(48) = ( {i}^(2) ) {}^(24) = 1 \\ \\ {i}^(49) = (i)( {i}^(48)) = (1 * i) = i`