If $\bar z$ be the conjugate of the complex number $z$, then which of the following relations is false
$|z|\, = \,|\bar z|$
$z.\,\bar z = |\bar z{|^2}$
$\overline {{z_1} + {z_2}} = \overline {{z_1}} + \overline {{z_2}} $
$arg\,z = arg\,\bar z$
$\left| {\frac{1}{2}({z_1} + {z_2}) + \sqrt {{z_1}{z_2}} } \right| + \left| {\frac{1}{2}({z_1} + {z_2}) - \sqrt {{z_1}{z_2}} } \right|$ =
$z_1$ and $z_2$ are two complex numbers such that $|z_1 + z_2|$ = $1$ and $\left| {z_1^2 + z_2^2} \right|$ = $25$ , then minimum value of $\left| {z_1^3 + z_2^3} \right|$ is
The amplitude of $\frac{{1 + \sqrt 3 \,i}}{{\sqrt 3 - i}}$ is
If $z$ is a complex number such that $\left| z \right| \ge 2$ , then the minimum value of $\left| {z + \frac{1}{2}} \right|$:
If the equation, $x^{2}+b x+45=0(b \in R)$ has conjugate complex roots and they satisfy $|z+1|=2 \sqrt{10},$ then