Question

Help me pleasssseeeeeee

Answer 1

Answer:

${ \bf{b. \: \: {i}^{47} }}$

Step-by-step explanation:

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

Answer 2

Answer:

$i^{46} = -i$

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

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

47/4 = 11 remainder 3 = 1

48/4 = 11 remainder 0 =  $i$

49/4 = 11 remainder 1 = -1

Step-by-step explanation:

$i = \sqrt{-1} = i$  (remainder 0)

$i^{2} = \sqrt{-1} * \sqrt{-1} = -1$ (remainder 1)

$i^{3} = \sqrt{-1} * \sqrt{-1} * \sqrt{-1}= -1 * \sqrt{-1} = -i$ (remainder 2)

$i^{4} = \sqrt{-1} * \sqrt{-1} * \sqrt{-1} * \sqrt{-1}= -1 * -1 = 1$ (remainder 3)

$i^{5} = \sqrt{-1} * \sqrt{-1} * \sqrt{-1} * \sqrt{-1}* \sqrt{-1}= 1 * \sqrt{-1} = i$ (remainder 0)

The pattern repeats every FOUR in the exponent