Question

Resolva a equação: z^4+(1+1)z^2+2(1-i)=0​

Answer 1

Resposta:

$z_1=\sqrt{\frac{-1-i+(\sqrt{-6+10i)} }{2} }\\\\z_2=\sqrt{\frac{-1-i+(\sqrt{-6+10i)} }{2} }$

Explicação passo-a-passo:

Seja a equação:

$z^{4}+(1+i)z^{2}+2-2i=0\\Seja:\\ z^{2}=y\\\\y^{2}+(1+i)y+2-2i=0\\Delta=(1+i)^{2}-4*1*(2-2i)\\Delta=2+2i-8+8i\\\\Delta=-6+10i\\\\\\y_1=\frac{-1-i+(\sqrt{-6+10i)} }{2} \\\\y_2=\frac{-1-i-(\sqrt{-6+10i)} }{2} \\\\Como::\\z^{2}=y\\\\z_1=\sqrt{\frac{-1-i+(\sqrt{-6+10i)} }{2} }\\\\z_2=\sqrt{\frac{-1-i+(\sqrt{-6+10i)} }{2} }$