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WHY d(z,w) = d(w,z) in Complex Numbers ℂ (SYMMETRY of the METRIC in ℂ as a METRIC SPACE)

YouTubeBill Kinney

WHY d(z,w) = d(w,z) in Complex Numbers ℂ (SYMMETRY of the METRIC in ℂ as a METRIC SPACE)

In this clip from my longer video on complex numbers as a metric space, we look at the symmetry property of the metric. For any two complex numbers z and w, the distance is defined by d(z,w) = |z - w|. It turns out that this metric is symmetric: d(z,w) = d(w,z). By writing z=x+iy and w=u+iv, we can see that the difference has real part x−u ...

171 views1 month ago

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