If $z_1$ and $z_2$ are two complex numbers satisfying the equation $\left|\frac{z_1+z_2}{z_1-z_2}\right|=1$, then $\frac{z_1}{z_2}$ may be

If $P(x)=0$ is a polynomial equation of least degree with integer coefficients and $\sqrt{2}+\sqrt{3} i$ is one of its roots,then that equation is

If $|z_1+z_2|^2=|z_1|^2+|z_2|^2$,where $z_1$ and $z_2$ are two complex numbers,then

$z_1, z_2, z_3$ represent the vertices $A, B, C$ of a triangle $ABC$ respectively in the Argand plane. If $|z_1-z_2|=\sqrt{25-12\sqrt{3}}$,$|\frac{z_1-z_3}{z_2-z_3}|=\frac{3}{4}$ and $\angle ACB=30^{\circ}$,then the area (in sq. units) of that triangle is

If $|z_1| = 2$,$|z_2| = 3$,$|z_3| = 4$ and $|2z_1 + 3z_2 + 4z_3| = 9$,then the value of $|8z_2z_3 + 27z_3z_1 + 64z_1z_2|$ is equal to:

If $a$ is a complex number and $b$ is a real number,then the equation $\bar{a}+a+b=0$ represents $a$ as a: