Question

Simplify to answer

Answer 1

\[\frac{ 7i-8 }{ i+1 }\]

Answer 2

Sure

Answer 3

multiply and divide by the conjugate of denominator
conjugate of i+1 is -i+1 (or 1-i)

Answer 4

How would you simplify it?

Answer 5

Ok but i'm getting i+15 for the answer and not forsure how they contained that

Answer 6

I don't need the answer right at this moment. I want to know how to work it out so if it is on a test I can work out it myself. Please just don't give me the answer. I am not learning anything from that

Answer 7

@HemerickLee what is the conjugate of
i + 1

Answer 8

(7i-8)(1-i)
you tried this for numerator, right ?

Answer 9

It would be -i+1...No I haven't

Answer 10

multiply and divide by the conjugate of denominator
conjugate of i+1 is -i+1 (or 1-i) as you rightly said.
so, \(\huge \dfrac{(7i-8)(-i+1)}{(i+1)(-i+1)}=...?\)

Answer 11

Factor it out right?

Answer 12

reverse of that.
multiply it out.
like (a+b)(c+d) = ab+ad+bc+bd

Answer 13

Ok so 7i times -i would give you......

Answer 14

7i * (-i) = -7i^2
and since, \(i=\sqrt{-1}, i^2=..... ?\)

Answer 15

i^2 would equal -1

Answer 16

So then for that one it would be 7

Answer 17

yes,
so +7 for that

Answer 18

7i times 1 would equal 7i. then -8 times -i would be?

Answer 19

-8 * (-i) = +8i
because -*-=+

Answer 20

i mean 2 negatives cancel each other :P

Answer 21

So all on top would be -7i^2+7i+8i-8

Answer 22

Then how about the bottom next

Answer 23

thats +7 +7i +8i -8
first simplify this, combine like terms, can you ?

Answer 24

where did the -7i^2 go?

Answer 25

as we already discussed
7i * (-i) = -7i^2 = +7 because i^2 = -1
right ?

Answer 26

I remember now. Typo sorry

Answer 27

So the top would become 15i-1.... Then I have some of the denominator started

Answer 28

yes,
simplify and tell me what u get for denominator.

Answer 29

for denominator,you can also use
(a+bi)(a-bi) = a^2-b^2 i^2 = a^2+b^2
so, (1+i) (1-i) =... ?

Answer 30

Uggghh, I got -i+1-1+1

Answer 31

Would that be right"?

Answer 32

@hartnn

Answer 33

It would result in 2.

Answer 34

yes, 2 is correct :)
sorry for late reply, my internet is not working properly.

Answer 35

NO that is fine my open study wasn't working a few minutes ago.... So the answer would be 15i-1 divided by 2

Answer 36

For all of my fraction ones with i can I just use the same thing that we did for all of them .

Answer 37

yes, (15i-1)/2 is correct.
yes, if there is a complex number in denominator, a+bi
you'll always multiply by the conjugate a-bi

Answer 38

(3i+4)/(i-7)... I used multiplying the top and bottom by the (-i+1)

Answer 39

in this case
denominator = i-7
its conjugate = -i -7
(just flip the sign of the term containing 'i')

Answer 40

So for all of them we multiply by the opposite of the bottom then?>

Answer 41

*conjugate of bottom

Answer 42

Alright thank you foryour help !

Answer 43

welcome ^_^