Express the complex number $\left(\frac{1}{1-4i}-\frac{2}{1+i}\right)\left(\frac{3-4i}{5+i}\right)$ in the standard form $a+ib$.

Express the complex number $\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$ in the standard form $a+ib$.

Find the real values of $x$ and $y$, if

$(x+iy)(2-3i)=4+i$

Find the real values of $x$ and $y$, if

$(3x-2iy)(2+i{)}^2=10(1+i)$

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

Find the real values of $x$ and $y$, if $(1+i)(x+iy)=2-5i$.

Find the conjugate of the complex number $4-5i$.

Find the conjugate of the complex number $\frac{1}{3+5i}$.