Showing that the distributive law holds in twizzle arithmetic is
equivalent to proving the trigonometric addition formulae.
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r1r2(cosq1 + i sinq1)(cosq2 + isinq2) |
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r1r2((cosq1cosq2-sinq1sinq2) + i(sinq1cosq2+cosq1cosq2)) |
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That's not the focus of this question though. What we're really
looking for is some experimentation with the animation leading
to an understanding of the behaviour of (z-i) , (z+i) , and (z-i)(z+i) as z moves in a loop-like path.
It's quite useful to look at the case where the beige
a -twizzle is zero in
the second animation.