Question

Show that if we identify the complex numbers $z, w$ with vectors in the plane, then their Euclidean dot product is equal to $\operatorname{Re}(z \bar{w})$.

   Show that if we identify the complex numbers $z, w$ with vectors in the plane, then their Euclidean dot product is equal to $\operatorname{Re}(z \bar{w})$.

Applied Linear Algebra (Undergraduate Texts in Mathematics)

Applied Linear Algebra (Undergraduate Texts in Mathematics)

Peter J. Olver,… 2nd Edition

Chapter 3, Problem 13

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Let $z = x + yi$ and $w = u + vi$, where $x, y, u, v$ are real numbers, and $i$ is the imaginary unit. Show more…

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Show that if we identify the complex numbers $z, w$ with vectors in the plane, then their Euclidean dot product is equal to $\operatorname{Re}(z \bar{w})$.

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