|a - b|^2 = (a - b)^2 \quad ext{if real, but not necessarily.}
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- Now compute \( |a - b| \). Note:
- |a - b|^2 = (a - b)(\overline{a} - \overline{b}) = |a|^2 - a\overline{b} - \overline{a}b + |b|^2
- But better to use algebra:
- |a - b|^2 = (a - b)(\overline{a} - \overline{b}) = |a|^2 + |b|^2 - a\overline{b} - \overline{a}b
- Not helpful unless complex conjugates known.
- Alternate: treat \( a \) and \( b \) as roots of quadratic:
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