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Commutativity.
Associative property of multiplication states that: (ab)c = a(bc) In words, no matter which order you multiply the numbers by, you obtain the same results.
Yes, for example (a + bi)(c + di) = ac + adi + bic + bidi, and commutative property works as well --> ac + adi + bci + bdi² --> ac + (ad + bc)i + bd(-1) = (ac - bd) + (ad + bc)i
The way in which numbers are grouped when added or multiplied does not change the sum or product.In symbols the associative property of addition says that (a+b) +c = a + (b +c) where a,b, and c are any numbers.The associative property for multiplication says that (ab)c=a(bc).Informally, the associative property says that grouping does not matter when applying the operation.
There is no distributive property of addition over multiplication. The equation works if a + (b * c) = (a + b)*(a + c) = a2 + ab +ac +bc => a + bc = a2 + ab +ac +bc ie a = a2 + ab + ac = a*(a+b+c) and that, in turn requires that a = 0 or a+b+c = 1 If a, b and c are fractions than the second condition requires the fractions to sum to 1 - not be equal to 1.