If $z_1 = 2 - 3i$ and the roots of the equation $z^3 + bz^2 + cz + d = 0$ are $i$,$z_1$,and $\bar{z}_1$,then $b + c + d =$

If $z=x+iy$ and $z^{1/3}=p+iq$,where $x, y, p, q \in R$ and $i=\sqrt{-1}$,then the value of $\left(\frac{x}{p}+\frac{y}{q}\right)$ is

Let $z$ be a complex number with a non-zero imaginary part. If $\frac{2+3z+4z^2}{2-3z+4z^2}$ is a real number,then the value of $|z|^2$ is:

If $Z_1, Z_2, Z_3$ are three complex numbers with unit modulus such that $|Z_1-Z_2|^2+|Z_1-Z_3|^2=4$,then $Z_1 \overline{Z_2}+\overline{Z_1} Z_2+Z_1 \overline{Z_3}+\overline{Z_1} Z_3=$

The minimum degree of a polynomial equation with rational coefficients having $\sqrt{3}+\sqrt{27}$ and $\sqrt{2}+5i$ as two of its roots is

Assertion $(A)$: If $z$ is a complex number such that $|z| \geq 3$,then the least value of $|z + \frac{3}{z}|$ is $1$.
Reason $(R)$: $|z_1 - z_2| \leq |z_1| + |z_2|$,for any two complex numbers $z_1, z_2$.
The correct option among the following is: