Let $Z$ and $W$ be complex numbers such that $\left| Z \right| = \left| W \right|,$ and arg $Z$ denotes the principal argument of $Z.$
Statement $1:$ If arg $Z+$ arg $W = \pi ,$ then $Z = -\overline W $.
Statement $2:$ $\left| Z \right| = \left| W \right|,$ implies arg $Z-$ arg $\overline W = \pi .$
Let $Z$ and $W$ be complex numbers such that $\left| Z \right| = \left| W \right|,$ and arg $Z$ denotes the principal argument of $Z.$
Statement $1:$ If arg $Z+$ arg $W = \pi ,$ then $Z = -\overline W $.
Statement $2:$ $\left| Z \right| = \left| W \right|,$ implies arg $Z-$ arg $\overline W = \pi .$
- [AIEEE 2012]
- A
Statement $1$ is true, Statement $2$ is false.
- B
Statement $1$ is true, Statement $2$ is true, Statement $2$ is a correct explanation for Statement $1$
- C
Statement $1$ is true, Statement $2$ is true, Statement $2$ is not a correct explanation for Statement $1.$
- D
Statement $1$ is false, Statement $2$ is true
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