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complex subsets

Source: LIMIT 2019 CBS2 P2

April 28, 2021
complex numbersalgebra

Problem Statement

Let C\mathbb C denote the set of all complex numbers. Define A={(z,w)∣z,w∈C and ∣z∣=∣w∣}A=\{(z,w)|z,w\in\mathbb C\text{ and }|z|=|w|\}B={(z,w)∣z,w∈C and z2=w2}B=\{(z,w)|z,w\in\mathbb C\text{ and }z^2=w^2\}<spanclass=′latex−bold′>(A)</span> A=B<span class='latex-bold'>(A)</span>~A=B <spanclass=′latex−bold′>(B)</span> A⊂B and A≠B<span class='latex-bold'>(B)</span>~A\subset B\text{ and }A\ne B <spanclass=′latex−bold′>(C)</span> B⊂A and B≠A<span class='latex-bold'>(C)</span>~B\subset A\text{ and }B\ne A <spanclass=′latex−bold′>(D)</span> None of the above<span class='latex-bold'>(D)</span>~\text{None of the above}
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