### * Multiplicative of complex numbers 8x8

 write me: ali.skalli.gva@gmail.com

A multiplicative square of complex numbers :

 3+11i -39+4i 4-7i -2+i -8+36i 5+3i -1-5i 9+7i 3-5i -4-32i -7-11i 5-i 16+11i 2+3i -7+i 3+16i 3+11i -3-i 7+3i -21+i -1+2i 13 -30-i 20 -20+17i -5+5i 6-2i 11+10i 1-3i 1-13i 17-7i 3-7i -1-8i -3-2i 1-13i -2-46i -3-i 3+11i 31+5i -5-i 1-13i 1-3i -1+5i -27+5i -7-9i 12+11i -14+18i -1-4i -4+8i 23+7i -13+13i -3+i 25-8i -1-17i -2+i 4-7i -2-5i -12-5i 3+16i -7+i -21+i 8+4i -1-3i 19-9i

The multiplicative magic constant is: - 26'509'600 + 97'193'200 i

Such a construction looks like a monstrosity requiring hours, or even days of computerized calculations. It is not the case at all. With my method, it is easy to infinitely and randomly generate such squares in a fraction of a second, using a simple spreadsheet software (you may download the Excel file at the bottom of this page).

In addition to appearing in the product of each line and row, the magic constant [- 26'509'600 + 97'193'200 i] appears in the product of the following remarkable combinations (by multiplying the values of the colored cells):

The diagonals and broken diagonals as follows :

Various figures:

 and so on…

Dispositions in pairs of 4x4 squares:

 and so on…

 write me: ali.skalli.gva@gmail.com

Ĉ
Ali Skalli,
Oct 14, 2009, 12:38 PM