Triangle Inequality

Consider a complex number $z$ satisfying $\left|z-3\right|+\left|z\right|+\left|z+3\right|=12$, then maximum value of $\left|z\right|$ is :

The minimum value of $\left|z+1\right|+\left|z-2\right|$ is equal to

If $\left|z-4+3i\right|\le 1$ and $\alpha$ and $\beta$ are the least and greatest value of $\left|z\right|$ and $k$ be the least value of  $\frac{x^4+x^2+4}{x}$ on the interval $\left(0,\infty \right)$, then $k$ is equal to -

If $\left|z-\frac{6}{z}\right|=2$, find the maximum value of $\left|z\right|$, where $z$ is a complex number.

For all complex numbers $z_1, z_2$ satisfying, $\left|z_1\right|=12$ and $\left|z_2-3-4 i\right|=5$; find the minimum value of $\left|z_1-z_2\right|$

Find the greatest value of $\left|z\right|$ when $\left|z-\frac{6}{z}\right|=2, z$ being a complex number.

Find the last value of $\left|z+\frac{1}{z}\right|$ if $\left|z\right|\ge 3$

If $\omega$ is a complex number satisfying $\left|\omega +\frac{1}{\omega }\right|=2,$ then maximum distance of $\omega$ from origin is

Let $z, w$ be two complex numbers such that $\left|z\right|=1$ and $\frac{w-1}{w+1}={\left(\frac{z-1}{z+1}\right)}^2$. Then maximum value of $\left|w+1\right|$ is

The maximum value of $\left|z\right|$, if $\left|z^2-3\right|=3\left|z\right|$, is

The minimum value of the expression $\left|3z-3\right|+\left|2z-4\right|$ is equal to (where, $z$ is a complex number)

If $z$ is a complex number satisfying $\left|z^3+z^{-3}\right|\le 2,$ then the maximum possible value of $\left|z+z^{-1}\right|$ is-

If $\left|z\right|\ge 3$ , then the least value of $\left|z+\frac{1}{4}\right|$ is

If z is complex number such that $\left|z-\frac{4}{z}\right|=2,$ then the greatest value of $\left|z\right|$ is

If z is a complex number, then the minimum value of $\left|z\right|+\left|z-1\right|$ is

Which of the following is incorrect for any two complex numbers $z_1$ and $z_2$?

If complex number $z_1$ and $z_2$ , $\arg \left(\frac{z_1}{z_2}\right)=0$ , then $\left|z_1-z_2\right|$ is equal to

The moduli of two complex numbers are less than unity, then the modulus of the sum of these complex numbers

If $z_1$ and $z_2$ are two complex numbers, then $\left|z_1-z_2\right|$ is