Question

Calcule: i²²¹ - i¹²³

Answer 1

Resposta:

2i

Explicação passo-a-passo:

Regra do expoente:

$\Rightarrow \displaystyle \mathsf{A^B+^C=A^BA^C}$

$\displaystyle \mathsf{i^2^2^1=i^2^2^0}\\\\\\\displaystyle \mathsf{i^{220}=\left(i^2\right)^{110}}\\\\\\\displaystyle \mathsf{i\left(i^2\right)^{110}}\\\\\\\displaystyle \mathsf{\left(-1\right)^{110}i}\\\\\displaystyle \mathsf{\left(-1\right)^{110}=1^{110}}\\\\\\\displaystyle \mathsf{1^1^1^0i}\\\\\\\displaystyle \mathsf{1^1^1^0=1}\\\\\\\displaystyle \mathsf{1i=i}\\\\\\\displaystyle \mathsf{i+i=2i}\\\\\\\Rightarrow \Large\boxed{\mathsf{2i}}$

i¹²³=i¹²²i

i(i²)⁶₁=(-1)⁶¹i

(-1)⁶¹=-1⁶¹

-1⁶¹i

1⁶¹=1

=-1i

1i=i

i-(-i)

Resolver.

i+i=2i

Em conclusão, a resposta final é 2i.

Espero que isso ajude você!