Prove that $(x+1+i)(x+1-i)(x-1-i)(x-1-i)=\left(x^4+4\right)$

Find the real values of $x$ and $y$ for which: $(1-i)x+(1+i)y=1-3i$

Find the real values of $x$ and $y$ for which: $(x+iy)(3-2i)=(12+5i)$.

Find the real values of $x$ and $y$ for which: $x+4yi=ix+y+3$.

Find the real values of $x$ and $y$ for which: $(1+i)y^2+(6+i)=(2+i)x$

Find the real values of $x$ and $y$ for which: $\frac{(x+3i)}{(2+iy)}=(1-i)$.

Find the real values of $x$ and $y$ for which: $\frac{(1+i)x-2i}{(3+i)}+\frac{(2-3i)y+i}{(3-i)}=i$.