Triangle Inequality

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 $\left|z\right|\ge 3$

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

Show that for any triangle with sides a, b, c $3(ab+bc+ca)\le (a+b+c{)}^2\le 4(ab+bc+ca).$

The set of all real numbers a such that $a^2+2a, 2a+3$ and $a^2+3a+8$ are the sides of a triangle is given by $a>$_____

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 $|z^2-1|=\left|z\right|+2$ , then

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

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

For any complex numbers $z_1 , z_2,$ the maximum value of $\frac{z_1{\overline{z}}_2+{\overline{z}}_1{z}_2}{\left|z_1\right|\left|z_2\right|}$ is

For any three complex numbers $z_1, z_2$ and $z_3;\mathrm{ }{z}_1\mathrm{Im}\left({\overline{z}}_2{z}_3\right)+z_2\mathrm{Im}\left({\overline{z}}_3{z}_1\right)+z_3\mathrm{Im}\left({\overline{z}}_1{z}_2\right)$ is equal to