Let $O$ be the origin and $A$ be the point $z _ { 1 } = 1 + 2i$. If $B$ is the point $z _ { 2 } , \operatorname { Re } \left( z _ { 2 } \right) < 0$, such that $OAB$ is a right angled isosceles triangle with $OB$ as hypotenuse, then which of the following is NOT true? (1) $\arg z _ { 2 } = \pi - \tan ^ { - 1 } 3$ (2) $\arg \left( z _ { 1 } - 2 z _ { 2 } \right) = - \tan ^ { - 1 } \frac { 4 } { 3 }$ (3) $\left| z _ { 2 } \right| = \sqrt { 10 }$ (4) $\left| 2 z _ { 1 } - z _ { 2 } \right| = 5$
Let $O$ be the origin and $A$ be the point $z _ { 1 } = 1 + 2i$. If $B$ is the point $z _ { 2 } , \operatorname { Re } \left( z _ { 2 } \right) < 0$, such that $OAB$ is a right angled isosceles triangle with $OB$ as hypotenuse, then which of the following is NOT true?\\
(1) $\arg z _ { 2 } = \pi - \tan ^ { - 1 } 3$\\
(2) $\arg \left( z _ { 1 } - 2 z _ { 2 } \right) = - \tan ^ { - 1 } \frac { 4 } { 3 }$\\
(3) $\left| z _ { 2 } \right| = \sqrt { 10 }$\\
(4) $\left| 2 z _ { 1 } - z _ { 2 } \right| = 5$