For any two non-zero complex numbers $z_1$ and $z_2$, if $|z_1+z_2|^2=|z_1|^2+|z_2|^2$, then

If $z = x + iy$ and $\arg\left( \frac{z - 2}{z + 2} \right) = \frac{\pi}{6}$,then the locus of $z$ is

If $|z| = 2$,then the points representing the complex numbers $-1 + 5z$ will lie on a

The area of $\Delta$ whose vertices are $z, \omega z, z + \omega z$ is (where $\omega$ is a complex cube root of unity):

If $|z - 3i| \le 5$,then the minimum value of $|z + 2|$ is equal to

$A$ function $f$ is defined on the complex numbers by $f(z) = (a + ib)z$,where $a, b \in \mathbb{R}^+$. This function has the property that the $f$-image of any point in the complex plane is equidistant from that point and the origin. If $|a + bi| = 10$ and $b^2 = \frac{p}{q}$,where $p, q \in \mathbb{Z}$ and $\text{gcd}(p, q) = 1$,then $p + q$ is: