Question

potência de i33 alguém sabe??​

Answer 1

Forma Universal:

$\sf \: i {}^{33} \\ \sf \: i {}^{32 + 1} \\ \sf \: i {}^{32} \times i {}^{1} \\ \sf \: 1i {}^{1} \\ \sf \: 1i {}^{} \\ \sf \: \boxed{\sf \: i}$

Forma polar:

$\sf \: i {}^{33} \\ \sf \: \Bigg( \cos\Bigg( \frac{\pi}{2} \Bigg) + i \times \sin\Bigg( \frac{\pi}{2} \Bigg)\Bigg) {}^{33} \\ \sf \: 1 {}^{33} \times \Bigg( \cos\Bigg(33 \times \frac{\pi}{2} \Bigg) + i \times \sin\Bigg(33 \times \frac{\pi}{2} \Bigg) \Bigg) \\\sf \: 1 \Bigg( \cos\Bigg( \frac{33\pi}{2} \Bigg) + i \times \sin\Bigg( \frac{33\pi}{2} \Bigg)\Bigg) \\ \sf \: 1\Bigg( \cos\Bigg( \frac{\pi}{2} + 2 \times 8\pi\Bigg) + i \times \sin\Bigg( \frac{\pi}{2} + 2 \times 8\pi\Bigg)\Bigg) \\ \sf \: 1\Bigg( \cos\Bigg( \frac{\pi}{2}\Bigg ) + i \times \sin\Bigg( \frac{\pi}{2} \Bigg)\Bigg) \\ \sf \: \boxed{\sf \: \cos\Bigg( \frac{\pi}{2} \Bigg) + i \times \sin\Bigg( \frac{\pi}{2} \Bigg)}$

Att: Nerd1990

Answer 2

Explicação passo-a-passo:

$\fbox{ i^{33}=i }$

divide o expoente 33 por 4 e eleva i ao resto

33 ÷ 4 = 32 com resto 1

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i¹ = i