Question

How do you simplify `( 8 - i ) ( 2 + i )`?

Answer 1

`17+6i`

Explanation:

By definition for complex numbers in rectangular form, if `(a;b)=a+ib and (x;y)=x+iy in CC`, then

`(a;b)*(x;y)=(ax-by;bx+ay)`

`=(ax-by)+i(bx+ay)`

So in this case, `(8;-1)*(2;1)=(8*2-(-1)*1;((-1)*2+8*1))`

`=(17;6)=17+6i`