Question

$resolver: (1+i)^{4i}$

Answer 1

Respuesta:

Explicación:

$(1+i)^{4i}\\\\ln[(1+i)^{4i}]= ln[(1+i)^{4i}]\\\\ln[(1+i)^{4i}]= 4i*ln[(1+i)]\\\\e^{ln[(1+i)^{4i}]} = e^{4i*ln[(1+i)]}\\\\(1+i)^{4i} = e^{4i*(ln|1+i|+i(\frac{\pi }{4}+2k\pi))}\\\\(1+i)^{4i} = e^{4i*(ln(\sqrt{2} )+i(\frac{\pi }{4}+2k\pi))}\\\\(1+i)^{4i} = e^{4i*(\frac{1}{2} ln(2 )+i(\frac{\pi }{4}+2k\pi))}\\\\(1+i)^{4i} = e^{2i*ln(2 )+4i*i(\frac{\pi }{4}+2k\pi)}\\\\(1+i)^{4i} = e^{2i*ln(2 )-\pi (1+8k)}\\\\(1+i)^{4i}= e^{2i*ln(2 )-\pi (1+8k)}\\\\(1+i)^{4i}= e^{i*ln(4 )-\pi (1+8k)}$

$(1+i)^{4i}= e^{-\pi (1+8k)}*[cos(ln(4))+isen(ln(4))]$

Answer 2

Respuesta:

Explicación:

$(1+i)^{4i}= e^{-\pi (1+8k)}*[cos(ln(4))+isen(ln(4))]$