Let Z and W be complex numbers such that |Z| | vedclass

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(B) Let $|Z| = |W| = r$. Then $Z = r e^{i	heta}$ and $W = r e^{i\phi}$,where $	heta = 	ext{arg } Z$ and $\phi = 	ext{arg } W$. Given $	heta + \ph

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Statement $1$ is true,Statement $2$ is true,Statement $2$ is a correct explanation for Statement $1$.

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(B) Let $|Z| = |W| = r$. Then $Z = r e^{i	heta}$ and $W = r e^{i\phi}$,where $	heta = 	ext{arg } Z$ and $\phi = 	ext{arg } W$. Given $	heta + \phi = \pi$,we have $	heta = \pi - \phi$. Thus,$Z = r e^{i(\pi - \phi)} = r e^{i\pi} e^{-i\phi} = -r e^{-i\phi}$. Since $\overline{W} = r e^{-i\phi}$,we get $Z = -\overline{W}$. So,Statement $1$ is true. For Statement $2$,$	ext{arg } \overline{W} = -	ext{arg } W = -\phi$. Then $	ext{arg } Z - 	ext{arg } \overline{W} = 	heta - (-\phi) = 	heta + \phi = \pi$. Thus,Statement $2$ is also true and explains Statement $1$.

Let $Z$ and $W$ be complex numbers such that $|Z| = |W|$,and $\text{arg } Z$ denotes the principal argument of $Z$.
Statement $1$: If $\text{arg } Z + \text{arg } W = \pi$,then $Z = -\overline{W}$.
Statement $2$: $|Z| = |W|$ implies $\text{arg } Z - \text{arg } \overline{W} = \pi$.

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Let $Z$ and $W$ be complex numbers such that $|Z| = |W|$,and $\text{arg } Z$ denotes the principal argument of $Z$.Statement $1$: If $\text{arg } Z + \text{arg } W = \pi$,then $Z = -\overline{W}$.Statement $2$: $|Z| = |W|$ implies $\text{arg } Z - \text{arg } \overline{W} = \pi$.