De Moivre's Theorem turns messy complex fractions into simple mental arithmetic!

De Moivre's Theorem turns messy complex fractions into simple mental arithmetic!
Multiply complex numbers without losing the imaginary part.
(a+bi)(c+di) = (ac − bd) + (ad + bc)i
No account. Formula shown. In-browser.
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Three lines moving on Lissajous curves. The colors come from a complex logarithm, implemented in a shader with Ollin's complex number helpers. Each pixel adds up the angles from one end of each line to the other.
S/N: 2026.012
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Can i^x = 2 ? 🤔
How can an imaginary base produce a real number ?
I explain it using Euler’s formula and complex numbers.
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