complex numbers

Really Complex Matrices

If you know how to multiply 2×2 matrices, and know about complex numbers, then you’ll enjoy this connection. Any complex number (a+bi) can be represented by a real 2×2 matrix in the following way! Let the 2×2 matrix [  a b ] [ -b a ] correspond...

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Chords of a Unit Circle

Take N equidistant points on the unit circle. Pick one of those points, then draw chords from it to all other points on the circle, as in Figure 1. What is the product of lengths of those chords?Surprise: for N points, the product is just...

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Complex Roots Made Visible

Everyone learns that the roots of a polynomial have a graphical interpretation: they’re the places where the function crosses the x-axis. But what happens when the equation has only imaginary roots? Do those have a graphical interpretation as well? Here’s an interpretation that works for quadratics. Take...

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