Question

Simplify into a + bi.
-9+8i/ 1 +2i

Answer 1

\[\large{\frac{-9+8i}{1+2i}}\]

Answer 2

Oh, don't you love making new accounts and posting the same question again and again?

Answer 3

Well, do you know about conjugates?

Answer 4

Well everyone was just bring rude, so I figured I would try again and see if someone serious would really help me.

Answer 5

No problem, fortunately , I am not going to be rude, unless you start making no effort, answer the question of parth.

Answer 6

Thank you mathslover for helping. I didn't mean you. :)

Answer 7

:) , though, I didn't help you yet,

Do you know about conjugates?

Answer 8

I am re-learning them. It has been a while. I have forgotten.

Answer 9

ok , so an introduction to conjugates (you need) :

\(\large{\color{blue}{\textbf{conjugate of a+bi will be :}} = \color{red}{a-bi}}\)

that is the + sin became - . Getting it?

Answer 10

Yes.

So -9-8i/1-2i?

Answer 11

No, see:

\(\large{\frac{a}{b} = \frac{ab}{b\times b} = \frac{ab}{b^2}}\)

right?

Answer 12

I suppose.

Answer 13

Right! so , \(\large{\color{blue}{\frac{-9+8i}{1+2i}}=\color{blue}{\frac{-9+8i}{1+2i}}\times \color{green}{\frac{1-2i}{1-2i}}}\)

What I did is : I just multiplied numerator and denominator with the conjugate of denominator i.e conjugate of 1+2i .

Answer 14

Can you tell me what is the conjugate of 1+2i ?

Answer 15

1-2i

Answer 16

good so that is what I multiplied. Getting it?

Answer 17

Yes.

Answer 18

So , can you tell me what will be :

\[\huge{\color{blue}{\frac{(-9-8i)(1-2i)}{(1+2i)(1-2i)}}}\]

Answer 19

oops there is -9+8i in the numerator.

Answer 20

Is that correct? Can I proceed?

Answer 21

-9-16i/1-2i.....Would that be correct?

Answer 22

\[\LARGE{\frac{(-9+8i)(1-2i)}{(1+2i)(1-2i)}}\]

First solve for this!

Answer 23

I did. :) Well I tried...

Answer 24

What you got in numerator?

Answer 25

I got -9-16i/-1-2i

Answer 26

I think you did mistake somewhere, well let us solve it!

Answer 27

(-9+8i)(1-2i)

^Let us first solve for numerator, OK? Ready?

Answer 28

Sorry. It is in there somewhere, I am just refreshing my memory. Haven't done these since high school.

Answer 29

Yes.

Answer 30

No problem, I am here to refresh dude, cool down.

OK, so : can you expand this : (-9+8i)(1-2i) ?

Answer 31

just like you do : (a+b)(c+d) = ac + ad + bc + bd

Expand (-9+8i)(1-2i) .

Answer 32

I don't get that.

Answer 33

ok , expand (2 + a)(3+b)

Answer 34

2 + a * 3 + b

Answer 35

See: use distributive property to expand : (2+a)(3+b)

2(3) + 2(b) +a(3) +a(b) = 6+2b+3a+ab

Getting it?

Answer 36

Slightly. It is kind of confusing.

Answer 37

hmn, do you know about distributive property?