Question

Calcule as potências de i

A) i50

B)6i51

Answer 1

A)

$i ^{50} \\ {i}^{48 + 2} \\ {i}^{48} \times {i}^{2} \\ {i}^{4 \times 12} \times {i}^{2} \\ ({i }^{4} ) {}^{12} \times {i}^{2} \\ {1}^{12} \times {i}^{2} \\ 1 \times {i}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 {i}^{2} = 1 \times ( - 1) = \boxed{ - 1}$

B)

${6i}^{51} \\ 6 \times {i}^{48 + 3} \\ 6 \times {i}^{48} \times {i}^{3} \\ 6 \times 1 {i}^{3} \\ 6 \times 1 \times ( - i) \\ 6 \times ( - i) \\ \boxed{ - 6i}$

$Espero \: ter \: Ajudado \\ MATEMÁTICA\\ \displaystyle\int_ \empty ^ \mathbb{C}     \frac{ - b \: ± \:  \sqrt{ {b}^{2} - 4 \times a \times c } }{2 \times a} d{ t } \boxed{ \boxed{ \mathbb{\displaystyle\Re}\sf{ \gamma  \alpha }\tt{ \pi}\bf{ \nabla}}}$