Question

Let \(C\) denote the set of all complex numbers.
Define \(A=\{(z, w) \mid z, w \in C\) and \(|z|=|w|\}, B=\left\{(z, w) \mid z, w \in C\right.\) and \(\left.z^{2}=w^{2}\right\}\). Then
(A) \(A=B\)
(B) \(A \subset B\)
(C) \(\mathrm{B} \subset \mathrm{A}\)
(D) \(\quad A \cap B=\varphi\)

Answer 1

Ans : (C)
Hint \(: z^{2}=w^{2}\)
$$
\begin{aligned}
&(z-w)(z+w) \\
&z=w,-w \\
&|z|=|w|
\end{aligned}
$$

Answer 2

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Answer 3

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