If $$a>0$$ and $$z=\frac{(1+i)^2}{a-i}, i=\sqrt{-1}$$, has magnitude $$\frac{2}{\sqrt{5}}$$, then $$\bar{z}$$ is

If $$(3 x+2)-(5 y-3) i$$ and $$(6 x+3)+(2 y-4) i$$ are conjugates of each other, then the value of $$\frac{x-y}{x+y}$$ is (where $$\left.i=\sqrt{-1}, x, y \in R\right)$$

The value of $$\frac{\mathrm{i}^{248}+\mathrm{i}^{246}+\mathrm{i}^{244}+\mathrm{i}^{242}+\mathrm{i}^{240}}{\mathrm{i}^{249}+\mathrm{i}^{247}+\mathrm{i}^{245}+\mathrm{i}^{243}+\mathrm{i}^{241}}, (\mathrm{i}=\sqrt{-1})$$ is

If $$|z-2+i| \leq 2$$, then the difference between the greatest and least value of $$|z|$$ is ________, $$(\mathrm{i}=\sqrt{-1})$$