The complex conjugate of $(4-3i)(2+3i)(1+4i)$ is

If $z$ is a complex number with $|z| \geq 5$,then the least value of $\left|z+\frac{2}{z}\right|$ is

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

If $(1 + i) \cdot (1 + 2i) \dots \dots \dots (1 + ni) = x + iy$ (where $i = \sqrt{-1}$), then find the value of $(2) \cdot (5) \cdot (10) \dots \dots \dots (1 + n^2)$.

If $\alpha, \beta$ are non-zero integers and $z=(\alpha+i \beta)(2+7 i)$ is a purely imaginary number,then the minimum value of $|z|^2$ is

If $z_1=1-2 i, z_2=1+i$ and $z_3=3+4 i$,then $\left|\left(\frac{1}{z_1}+\frac{2}{z_2}\right) \frac{z_3}{z_2}\right|=$