Question

o valor da divisão (i+4) elevado a 4 \ (i-2)²

Answer 1

$(i + 4)^{4}$ ÷ $(i - 2)^{2}$

$\frac{(i + 4)^{4} }{(i - 2)^{2} }$

$\frac{161 + 240i}{i^{2}- 4i + 4 }$

$\frac{161 + 240i}{3-4i}$

R= $-\frac{477}{25} + \frac{1364}{25}i$

 Forma alternativa:

 $-19,08 + 54,56i$

Answer 2

Resposta:

(i+4)⁴ =[(i+4)²]² =[i²+8i+16]²=[-1+8i+16] ² =[8i+15]² =64i²+240i+225

=-64+240i +225 =161 +240i

(i-2)² =i²-4i+4 =-1-4i+4=3-4i

= (161 +240i)/(3-4i) = (141 +240i)(3+4i) /(3-4i)(3+4i)

= (161 +240i)(3+4i) /(3²-16i²)

= (483 +720i+644i+960i²)/(9+16)

= (483 +720i+644i-960)/(9+16)

=(1364i-477)/25

= -477/25 +1364i/25