If $x = 1 + 2i$,then the value of $x^3 + 7x^2 - x + 16$ is

If $(1 + i)(1 + 2i)(1 + 3i) \dots (1 + ni) = a + ib$,then $2 \times 5 \times 10 \times \dots \times (1 + n^2)$ is equal to

Let $A = \{\theta \in (0, 2\pi) : \frac{1+2i \sin \theta}{1-i \sin \theta} \text{ is purely imaginary} \}$. Then the sum of the elements in $A$ is

If $\cos A+\cos B+\cos C=0$ and $\sin A+\sin B+\sin C=0$,then $\cos (A-B)=$

Let $z$ be a complex number satisfying $|z|^3 + 2z^2 + 4\bar{z} - 8 = 0$,where $\bar{z}$ denotes the complex conjugate of $z$. Let the imaginary part of $z$ be non-zero.
Match each entry in List-$I$ to the correct entries in List-$II$.

List-$I$	List-$II$
$(P)$ $|z|^2$ is equal to	$(1)$ $12$
$(Q)$ $|z-\bar{z}|^2$ is equal to	$(2)$ $4$
$(R)$ $|z|^2+|z+\bar{z}|^2$ is equal to	$(3)$ $8$
$(S)$ $|z+1|^2$ is equal to	$(4)$ $10$
	$(5)$ $7$

If $z = x - iy$ and $z^{1/3} = p + iq$ $(x, y, p, q \in R)$, then $\frac{(\frac{x}{p} + \frac{y}{q})}{(p^2 + q^2)}$ is equal to