Multiplying Tuples (ordered pairs)

[The Student]

My notes state that (a,b) · (c,d) = (ac − bd,ad + bc). This does not work when a = 1, b = 2, c = 3, d = 4. Does that multiplication make sense to anyone? How is it true?

 

[Romsek]

My notes state that (a,b) · (c,d) = (ac − bd,ad + bc). This does not work when a = 1, b = 2, c = 3, d = 4. Does that multiplication make sense to anyone? How is it true?

This is for complex numbers. Your tuples (a,b) stand for a + i b where i = sqrt(-1)

Multiplying two complex numbers (a,b) and (c,d) gives you

(a + i b)(c + i d) = (ac - bd) + i(ad + bc) --> (ac-bd, ad+bc). The key here is that i * i = -1

 

[The Student]

This is for complex numbers. Your tuples (a,b) stand for a + i b where i = sqrt(-1)

Multiplying two complex numbers (a,b) and (c,d) gives you

(a + i b)(c + i d) = (ac - bd) + i(ad + bc) --> (ac-bd, ad+bc). The key here is that i * i = -1

Oh thank-you, that makes sense.