We have seen that complementary numbers add up to a power of 10. Partially complementary numbers have their first digits common (the root), and their last digits (suffix) add up to a power of 10. For example, 43 and 57 are complementary, because 43 and 57 add up to 100, a power of 10. On the other hand, 343 and 357 are partially complementary, the root is 3 and the suffices are 43 and 57.
To calculate the product, you would have to calculate product of the root and the next number, and append the product of the suffices.
To multiply 53 by 57, we identify that the root is 5 and the suffices are 3 and 7. The product of the root and the next number is therefore 5*(5+1)=30. Appending the product of 3 and 7 (=21) to 30 gives 3021. Thus 53*57 = 3021.
Note that this is almost the same procedure as the calculation of squares of numbers ending in 5. Instead of appending 25, we append the product of the suffices.
The same steps will be followed. Multiply the root by the next number. Append the product of the suffices.
For example, for 1545*1555, the root is 15, suffices are 45 and 55. Thus the product of the root and the next number is 15*(15+1)=240. To this, we append the product of the suffices, 45*55=2475. The suffices here are two digits long, and their product must therefore occupy four digits. Thus 1545*1555=2402475.