$\sinh(ix)$ is equal to

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 $p^2=$

If $z$ is a complex number such that $|z+4| \geq 3$,then the smallest value of $|z+3|$ is

If $|z + 1| = \sqrt{2} |z - 1|$,then the locus described by the point $z$ in the Argand diagram is a

If $|z^2 - 1| = |z|^2 + 1$,then $z$ lies on

Let $z_{1}$ and $z_{2}$ be two fixed complex numbers in the Argand plane and $z$ be an arbitrary point satisfying $|z-z_{1}|+|z-z_{2}|=2|z_{1}-z_{2}|$. Then,the locus of $z$ will be