Question

Calculați
Numere complexe​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Explicație pas cu pas:

$(1+i)^{2n}+(1+i)^{2n+1}=$

$=(\sqrt{2}e^{i\frac{\pi}{4}})^{2n}+(\sqrt{2}e^{-i\frac{\pi}{4}})^{2n+1}=$

$=2^n[(e^{i\frac{\pi}{2}})^n+(1-i)(e^{-i\frac{\pi}{2}})^n]=$

$=2^n[i^n+(1-i)(-i)^n]=$

$=\begin{cases}2^n(2-i)&\text{dacă }n\equiv 0(\text{mod } 4)\\-2^n&\text{dacă }n\equiv 1(\text{mod }4)\\2^n(-2+i)&\text{dacă }n\equiv 2(\text{mod } 4)\\2^n&\text{dacă }n\equiv 3(\text{mod } 4)\end{cases}.$