The conjugate of the complex number $\frac{2 + 5i}{4 - 3i}$ is

If $z = \frac{4}{1-i}$, then $\bar{z}$ is (where $\bar{z}$ is the complex conjugate of $z$).

Let $z$ be a complex number such that $|z|+z=2+i$,where $i=\sqrt{-1}$. Then $|z|$ is equal to:

If $(\sqrt{8} + i)^{50} = 3^{49}(a + ib)$,then $a^2 + b^2$ is

If the conjugate of $(x + iy)(1 - 2i)$ is $1 + i$,then:

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