Question

Help on this two step problem

Answer 1

Can you tell me the complex conjugate of 2+i
if I tell you the complex conjugate of a+bi is a-bi?

Answer 2

2-i

Answer 3

Right so that is what you are going to multiply on top and bottom

Answer 4

so multiply the problem by 2-i

Answer 5

you need to compute both of these products
\[(6-3i)(2-i)=? \\ (2+i)(2-i)=?\]

Answer 6

You can use "foil method" if you wish

Answer 7

basically you are going to take every term in the first ( ) and multiply it to every term in the second ( )

Answer 8

after that it is combining like terms

Answer 9

let's look at the first product together

Answer 10

(6-3i)(2-i)

Can you tell me what you get when you multiply 6 to 2 and 6 to -i ?
And also tell me what you get when you multiply -3i to 2 and -3i to -i?

Answer 11

Recall i^2=-1

Answer 12

Okay the first one is 9-12i and the second is 5

Answer 13

let's check

(6-3i)(2-i)
6 to both terms in (2-i)
-3i to both terms in (2-i)
so this gives us
12-6i-6i+3i^2
9-12i
first product is right
you go!

now let's check second pruduct
(2+i)(2-i)
you can actually shortcut this one since you are multiplying conjugates or do the long way which is describe above
4-i^2
4+1
5 is right!

Answer 14

So you have
\[\frac{9-12i}{5}\]

Answer 15

Yup that is what I got

Answer 16

does that complete step 1?

Answer 17

That is step 1 and step 2
you are finished

Answer 18

wait I have to write it separate. so step one is what?

Answer 19

just multiplying

Answer 20

not anything else for step 1

Answer 21

you start adding or combining like terms in step 2

Answer 22

and replacing i^2 with -1 as suggested

Answer 23

and then step 2?

Answer 24

multiplying (do not add) in step 1


replace i^2 with -1 and combine like terms on your top and combine like terms on your bottom for step 2

Answer 25

so multiplying it by 2-i right for step 1

Answer 26

yep on top and bottom

Answer 27

nd then the answer to that

Answer 28

step 1 for numerator: example of multiplying (6-3i)(2-i)=12-6i-6i+3i^2

step 2 for numerator: example if replacing i^2 with -1 and combining like terms
12-12i+3(-1)
12-12i-3
9-12i

just go back and put the denominator in both steps

Answer 29

OKay thanks