Wednesday, June 24, 2009

Class today

(3i+1)(5+2i)




M u l t i p l y i a n d 3

M u l t i p l y i a n d 1

T h e i j u s t g e t s c o p i e d a l o n g .

T h e a n s w e r i s i

i

3 * i e v a l u a t e s t o 3 i

3 * i + 1 e v a l u a t e s t o 3 i + 1

M u l t i p l y i a n d 2

M u l t i p l y i a n d 1

T h e i j u s t g e t s c o p i e d a l o n g .

T h e a n s w e r i s i

i

2 * i e v a l u a t e s t o 2 i

5 + 2 * i e v a l u a t e s t o 5 + 2 i

M u l t i p l y i n g 3 i + 1 b y 5 + 2 i i s a c l a s s i c A l g e b r a p r o b l e m .
H e r e , y o u a r e t r y i n g to m u l t i p l y t w o b i n o m i a l s t o g e t h e r
( t w o e x p r e s s i o n s t h a t e a c h c o n t a i n t w o t e r m s ) .
Y o u r b o o k m i g h t c a l l t h i s f i n d i n g t h e " P r o d u c t o f T w o
B i n o m i a l s " .

T o w o r k t h i s p r o b l e m , w e ' l l u s e t h e " F . O . I . L . " m e t h o d .
F . O . I . L . s t a n d s f o r F i r s t , O u t e r , I n n e r , L a s t .

F i r s t , w e ' l l m u l t i p l y t h e t w o F i r s t t e r m s , t h e 3 i a n d 5
t o g e t h e r .

M u l t i p l y 3 i a n d 5

M u l t i p l y i a n d 1

T h e i j u s t g e t s c o p i e d a l o n g .

T h e a n s w e r i s i

i

3 i ◊ 5 = 1 5 i

S e c o n d , w e ' l l m u l t i p l y t h e t w o O u t e r t e r m s , t h e 3 i a n d
2 i t o g e t h e r .

M u l t i p l y 3 i a n d 2 i

M u l t i p l y i a n d i

C o m b i n e t h e i a n d i b y a d d i n g t h e e x p o n e n t s , a n d k e e p i n g
t h e i , t o g e t

T h e a n s w e r i s

3 i ◊ 2 i =

T h i r d , w e ' l l m u l t i p l y t h e t w o I n n e r t e r m s ,
t h e 1 a n d 5 t o g e t h e r .

M u l t i p l y 1 a n d 5

1

1 ◊ 5 = 5

L a s t l y , w e ' l l m u l t i p l y t h e t w o L a s t t e r m s , t h e 1 a n d 2 i
t o g e t h e r .

M u l t i p l y 1 a n d 2 i

M u l t i p l y 1 a n d i

T h e i j u s t g e t s c o p i e d a l o n g .

i

1 ◊ 2 i = 2 i

1 5 i c o m b i n e s w i t h 2 i t o g i v e 1 7 i

( 3 * i + 1 ) * ( 5 + 2 * i ) e v a l u a t e s t o

T h e f i n a l a n s w e r ( a l m o s t ! ) i s...

N o w , l e t ' s s i m p l i f y t h e i ' s t o g e t o u r f i n a l a n s w e r :
T h e i i n 1 7 i c a n n o t b e s i m p l i f i e d , s o j u s t l e a v e i t a s i s .

T h e i 2 i n c a n b e s i m p l i f i e d t o - 1 .

S o , t h e b e c o m e s - 6 .

- 6 c o m b i n e s w i t h 5 t o g i v e - 1

T h e f i n a l a n s w e r i s
1 7 i - 1





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2 comments:

Fred Wishnie said...

Are you sure there's not something funny in your water? You've been particularly obtuse the last few days.

Jeff said...

What?.....