Triangle Inequality

The minimum value of $|z-3|+|z-4i|$ is

If $|z-4+3i|\le 2$, then the least and the greatest values of $\left|z\right|$ are

For any complex number $z$, the minimum value of $\left|z\right|+|z-3 i|$ is

Which of the following statements is(are) correct.

If $z$ is a complex number and the minimum value of $\left|z\right|+|z-1|+|2z-3|$ is $k$ if $\beta =2\left[\alpha \right]+3=3[\alpha -k]$ then (where $[.]$ denotes the greatest integer function)

If $z\in C$ and $|z{|}^2-2|z|-3<0$, then the possible value(s) of $\left|z^2+2z\cos \theta \right|$ for all values of $\theta$ is(are)

If $z\in C$ and $|z{|}^2-2|z|-3<0,$ then the possible value(s) of $\left|z^2+2z\cos \theta \right|$ for all values of $\theta$ is(are)

Let complex number $z$ satisfy $\left|z-\frac{2}{z}\right|=1,$ then $\left|z\right|$ can take all values except

If $z$ satisfies $|z-1|<|z+3|,$ then $\omega =2z+3-i$ satisfies

For all the complex numbers $z_1,z_2$ satisfying $\left|z_1-3\right|=3$ and $\left|z_2-3+18i\right|=2$ then the minimum value of $\left|z_1-z_2\right|$ is equal to

The maximum value of $\left|z\right|$where $z$satisfies the condition $\left|z+\frac{2}{z}\right|=2$, is

Let $z_1, z_2$ be two complex numbers represented by points on the circle $\left|z\right|=1$ and $\left|z\right|=2$ respectively, then