sorry to flood the forum I have another a+ b(i) problem

[moronatmath]

ok can someone please fill me in on were I am going wrong on this problem?

Evaluate the expression (-1+ 3i)+(2 + 2i) and write the result in the form a+ b i

ok so I foiled
-1*2+3i*2-1*2i+3i*2i
=
-2+6i-2i+6i
=
-2+10i
so a=-2 b=10
Unfortunatly this is wrong and I have no clue were I messed up. If I had to guess I was suppose to plug in the + somewhere from the origional "expression".

Please help me out!

 

[galactus]

I think I see where you "flubbed your dub".

\(\displaystyle (-1+3i)(2+2i)\)

\(\displaystyle {-1}*2={-2}\; -1*2i={-2i}\; 2*3i=6i\; 3i*2i=6i^{2}\)

We have:

\(\displaystyle 6i^{2}+4i-2\), See?.

 

[moronatmath]

I am not sure? a does not equal 2,4 or 6. What would you you say
a and b = ?????

I appreciate the reply!

 

[galactus]

Well, since \(\displaystyle i^{2}=-1\) you have -6.

-6+-2=-8. So you have \(\displaystyle {-8}+4i\). NOw, you see?.

 

[pka]

You have written an addition problem: (-1+ 3i)+(2 + 2i)
(-1+ 3i)+(2 + 2i)=1+5i, a=1 & b=5.

But if it is a multiplication problem: (-1+ 3i)(2 + 2i)=(−2−6)+( −2+6)i.

Which is it?

 

[moronatmath]

It is an addition problem for sure.

 

[galactus]

I thought it was multiplication. Why are we FOILing?. Just add them up.

 

[pka]

“FOIL” Damn I hate FOIL
Foil is what I wrap my grill to smoke meat.

The first time I ever hear the term was at a ‘parent's night’.
Oddly enough, my daughter’s teacher was giving a demonstration.
She used that expression! Because I was horrified, I asked her that evey night to do this, (x+y+z)<SUP>2</SUP>. She could not do it.
Latter, she was my graduate student and got a Masters with me.
We did get that error straight: DO NOT USE FOIL.

 

[galactus]

I know, pka, FOIL is a 'rookie' technique. But most every student is

familiar with it. Since it is a bugaboo of yours, pka, I will stop using it.

Okey-doke?

 

[pka]

a bugaboo of yours, pka…

That is just not the point!
Do you see that the teacher could not do (x+y+z)<SUP>2</SUP>?
FOIL has become such a crutch that it is a be all and end all for factoring/multiplying.
Why not teach multiplication by practice. Allow the student to discover ‘FOIL”.
It only works for binominals.
Why do we make students totally dependent on algorithms?
We are lying we when we say that we are teaching students ‘critical thinking’, yet we give then comfortable algorithms such as ‘FOIL”.
Teachers who use 'FOIL" are just lazy!

 

[Mrspi]

Answer to student's question

After all the ranting about FOIL, did anyone bother to answer the student's question??

If this is an ADDITION problem, it is of the form

(a + bi) + (c + di)

Addition has the commutative and associative properties. You can re-order and re-group the terms:

(a + c) + (bi + di)
(a + c) + (b + d)i

It's as simple as this: add the real parts, add the imaginary parts, and write the sum in the form
real + imaginary

 

[pka]

Re: Answer to student's question

After all the ranting about FOIL, did anyone bother to answer the student's question??

Really Mrspi, I expected more of you!
Did you even bother to read the complete thread?
If you did, how could have asked such a question?

 

[Mrspi]

Re: Answer to student's question

Did you even bother to read the complete thread?
If you did, how could have asked such a question?

Yup, I did. And I didn't see a clear explanation of how one adds two complex numbers.

And though I'm one of those teachers who has used the dreaded FOIL, I always taught it as a shortcut for the distributive property in the case of multiplying two binomials....please don't tar all teachers with the same brush.