multiplication of ordered pairs

$\begingroup$

From what I've seen, ordered pair multiplication is $(a,b) \times (c,d) = (ac-bd,ad+bc)$.

Also, $(0,1)$ represents $i$. So if I wanted to take $(0,-1) \times (0.-1)$, that would be $= (-1,0)$, right?

Which means $-i^2 = -1$. But $-i^2 = 1$! Where am I going wrong?

$\endgroup$ 0

2 Answers

$\begingroup$

It looks like you're failing to distinguish between $(-i)^2$ and $-(i^2)$. The former is $-1$ (it always holds that $(-a)^2=a^2$ in a ring); the latter is $1$.

$\endgroup$ $\begingroup$

You are taking symbols wrong. It should be $(-\iota)^2$ and $-(\iota)^2$.

$\endgroup$ 2

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy