For the real parameter $t$, the locus of the complex number $z = (1 - t^2) + i \sqrt{1 + t^2}$ in the complex plane is

Let $A$ and $B$ represent $z_1$ and $z_2$ in the Argand plane and $z_1, z_2$ be the roots of the equation $Z^2+pZ+q=0$,where $p, q$ are complex numbers. If $O$ is the origin,$OA=OB$ and $\angle AOB=\alpha$,then $p^2=$

The locus of $z$ satisfying $\left|\frac{z-i}{z-2i}\right|=2$ is a

$ABCD$ is a rhombus. Its diagonals $AC$ and $BD$ intersect at the point $M$ and satisfy $BD = 2AC$. If the points $D$ and $M$ represent the complex numbers $1 + i$ and $2 - i$ respectively,then $A$ represents the complex number

If the area of the triangle formed by the points $z, z + iz$ and $iz$ on the complex plane is $18$,then the value of $|z|$ is

If $z$ is a complex number satisfying $|z - 3| \leq 5$,then the range of $|z + 3i|$ is (where $i = \sqrt{-1}$).