If $z$ is a complex number, then which of the following is not true

If $\sqrt 3 + i = (a + ib)(c + id)$, then ${\tan ^{ - 1}}\left( {\frac{b}{a}} \right) + $ ${\tan ^{ - 1}}\left( {\frac{d}{c}} \right)$ has the value

Let $z _{1}$ and $z _{2}$ be two complex numbers such that $\overline{ z }_{1}=i \overline{ z }_{2}$ and $\arg \left(\frac{ z _{1}}{\overline{ z }_{2}}\right)=\pi$. Then

If $0 < amp{\rm{ (z)}} < \pi {\rm{,}}$then $amp(z)-amp ( - z) = $

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

Let $z_1$ and $z_2$ be two complex number such that $z_1$ $+z_2=5$ and $z_1^3+z_2^3=20+15 i$. Then $\left|z_1^4+z_2^4\right|$ equals-