Reply to comment Thanks to A Moss for bringing this puzzle to
our attention. This puzzle concerns complex numbers but don't
worry. You don't need to know anything about complex numbers to
solve it! A complex number is often written as the sum of a real
and an imaginary part as follows: i is a symbol representing the
square root of minus one (sometimes j is used instead), a is the
real part and b is the imaginary part. a and b are both real
numbers. Suppose that we have two complex numbers that we wish
to multiply together to make a third. If we expand the brackets
on the right hand side we get the following expression: But as
i2 is minus one (by definition) we can reduce this to the
following two expressions for p and q: This process of
multiplying two complex numbers together is something which the
computer programs that generate those beautiful fractal images
you so often see in books must do over and over again.
Traditionally, computers have been able to add and subtract much
faster than they can multiply