Question

(3 + 6i) x (2 +9i)

Answer 1

-48 +39i

Answer 2

\[(a+bi)(c+di)=(ac-bd)+(ad+bc)i\] is the cowboy way to do it

Answer 3

6+30 i-54 = 48 +30 i

Answer 4

-48+39 i

Answer 5

\[6+27i+12i-54\]\[39i-48\]

Answer 6

I mean -48 +30 i

Answer 7

I used the FOIL method, and got 6+39i + 54i^2 is that right?

Answer 8

yes

Answer 9

i^2=-1

Answer 10

in your head :
\[6-54=-48\]
\[27+12=39\] answer
\[-48+39i\]

Answer 11

Isn't i^2= -1?

Answer 12

:D yess

Answer 13

That changes things - hang on...

Answer 14

Now I get 39i - 48

Answer 15

yes that is why the real part is
\[ac-bd\] instead of
\[ac+bd\]

Answer 16

that is right. but "standard form" is
\[a+bi\] so write
\[-48+39i\]

Answer 17

Thanks!

Answer 18

one more - posting in a second!

Answer 19

@jenn if you are going to do a lot of these, i would suggest remembering that it is
\[(ac-bd)+(ad+bc)i\] although you can also use "foil" and then say "oh look, i squared is -1"