Question

PRE CALC HELP!!!
Compute;
(-3+2i)/(4+11i)

Answer 1

\[\frac{-3+2i}{4+11i}\\
=\frac{-3+2i}{4+11i}\times\frac{4-11i}{4-11i}\\
=\]

Answer 2

Okay so basically we are doing cross multiplication here?

Answer 3

we are multiplying the denominator by its complex conjugate, this will realize the denominator

Answer 4

alright makes sense

Answer 5

i'm gonna go smack every math teacher that ever said "cross multiply"

Answer 6

It helps me to remember when dealing with fractions

Answer 7

what does the new denominator become
\[(4+11i)\times(4-11i)=?\]

Answer 8

8+122i

Answer 9

becasue we get 1-44i+44i-122i

Answer 10

try that again

Answer 11

\[(a+b)(a-b) = a^2-b^2\]

Answer 12

and also (which is what you need ) \[(a+bi)(a-bi)=a^2+b^2\]

Answer 13

What happened to your SmartScore @satellite73?

Answer 14

Im very lost now

Answer 15

Like what numbers are a and b in this case?

Answer 16

a = 4

b = 11i

Answer 17

(4+11i)(4-11i)=4^2+11i^2

Answer 18

almost
\[(4+11i)(4-11i)=4^2-11i^2\]

now use \(i^2=-1\)

Answer 19

16+11=27*

Answer 20

whoops

i mean
\[(4+11i)(4-11i)=4^2-(11i)^2\]

Answer 21

so its 16-11?

Answer 22

so \[4^2-11^2i^2=4^2+11^2\]

Answer 23

Oh so then 16+122

Answer 24

yes, the denominator becomes 16 + 121

Answer 25

137

Answer 26

So, you have\[\frac{-3+2i}{4+11i}\\
=\frac{-3+2i}{4+11i}\times\frac{4-11i}{4-11i}\\
=\frac{(-3+2i)(4-11i)}{4^2+11^2}\\
=\frac{(-3+2i)(4-11i)}{137}\\
=\]

Answer 27

Now simplify the numerator

Answer 28

\[(a+b)(c+d) = ac+ad+bc+bd\]

Answer 29

now
a = -3,
b = 2i,
c = 4,
d = -11i

Answer 30

(-3(4)+-3(-11i)+2i(4)+2i(-11))/137

Answer 31

yeap, now simplify it

Answer 32

(-12+33i+8i-22i)/137

Answer 33

good, keep going

Answer 34

(-12+19i)/137

Answer 35

oh wait, the last term should have an i^2


(-3(4)+-3(-11i)+2i(4)+2i(-11i))/137


(-12+33i+8i-22i^2)/137

Answer 36

right?

Answer 37

Yeah

Answer 38

and we know that i^2=−1

(-12+33i+8i+22)/137

Answer 39

okay cool

Answer 40

63i-12/137

Answer 41

not quite

Answer 42

but 33+6+22=63 and the -12 goes with it

Answer 43

-12+63i

Answer 44

you can only add the like terms, the 33i and 8i are like terms, and the -12 and +22 are like tems

Answer 45

oh lol I forgot that the i^2 went away oops

Answer 46

41i+10/137

Answer 47

i think then you do 41i/137, 10/137

Answer 48

Either of those two forms the final result. Well done. \(\color{red}\checkmark\)

Answer 49

sweet thanks for the help