Let $Z$ and $W$ be complex numbers such that $| Z | = | W |$, and $\arg Z$ denotes the principal argument of $Z$. Statement 1: If $\arg Z + \arg W = \pi$, then $Z = - \bar { W }$. Statement 2: $| Z | = | W |$, implies $\arg Z - \arg \bar { W } = \pi$. (1) Statement 1 is true, Statement 2 is false. (2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1. (3) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1. (4) Statement 1 is false, Statement 2 is true.
Let $Z$ and $W$ be complex numbers such that $| Z | = | W |$, and $\arg Z$ denotes the principal argument of $Z$. Statement 1: If $\arg Z + \arg W = \pi$, then $Z = - \bar { W }$. Statement 2: $| Z | = | W |$, implies $\arg Z - \arg \bar { W } = \pi$.\\
(1) Statement 1 is true, Statement 2 is false.\\
(2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.\\
(3) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.\\
(4) Statement 1 is false, Statement 2 is true.