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124 THE FASCINATION OF NUMBERS

numbers and the multiplication of these parts may be shown
as follows:

I4=1-+413 I X13=1I3
=2+12 2 X12=24
=311 3 XI11=33
=4-+10 4 X10=40
mann DX J=45
=6+ 8 6x 8=48
Y T 40

No higher quotient is possible since the next stage is 8 x6,
and this is the same as the sixth stage shown above. The
number 14 cannot, therefore, be split into two integral parts
so that the multiplication of these parts results in a number
greater than 49.

If we introduce imaginary numbers, however, the number
14 can be split into two parts to give any result we like:

If 7+7=14
Then (7+V —10)+(7—V —10) =14
for we have added v/ —10 and taken it away again. And,

(74 v —10) multiplied by (7 —4/ —10) =49—V/(—10)?2
=49+ 10
=59 or 39