Im so bad with math...somebody plz help/ Multiply (5 + 2i)(3 - 4i).?

To best explain this, I'd like to start with an easier example:

1. 5*4i

This is probably very familiar to you, here you multiply like terms, so 4 times 5 is 20 and i doesn't have a like term so it doesn't change.

= 20i

2. 5i*4i

Same deal. 5*4 = 20 and i*i = i^2

= 20i^2

3. 5(3-4i)

Here you must use the distributive property. 5 is being multiplied by each term in the brackets:

5(3-4i) = 5*3 - 5*4i = 15 - 20i

4. 2i (3-4i)

Let's try it again.

2i*3 - 2i*4i = 6i - 8i^2

5. Now we can try the problem:

(5 + 2i)(3 - 4i)

Using the distributive property:

5(3-4i) + 2i(3-4i)

Use the distributive property again

( 5*3 - 5*4i ) + ( 2i*3 - 2i*4i)

Now you just need to multiply through

(15 - 20i) + (6i - 8i^2)

I was only using brackets for clarity, so we can take them away (but remember if there was a negative sign in front of a term in brackets you must use the distributive property again:

eg. -(2-3) = -1(2-3) = -1*2 - -1*3 = -2+3 ) Back to the point:

15 - 20i +6i - 8i^2

Now you can add like terms.

15 - 14i - 8i^2

And this is your answer.

When we started you could have also expanded like this:

(5 + 2i)(3 - 4i)

= 3(5 +2i) - 4i(5 + 2i)

= (3*15 + 3*2i) - (4i*5 + 4i*2i)

= (15 + 6i) - (20i + 8i^2)

Remember the negative sign here

= 15 + 6i -20i - 8i^2

= 15 -14i - 8i^2

The answer will be the same no matter how you tackle it as long as you follow the rules.

It can look complicated at first, but once you master the rules, you'll find math easy.

Good luck!

(5 + 2i)(3 - 4i)

To do this, you need to use FOIL: multiply the First, Outer, Inner, and Last terms together from each binomial (2-terms)

First: 5*3 = 15

Outer: 5*-4i = -20i

Inner: 2i*3 = 6i

Last: 2i*-4i = -8i^2

So, after FOILing, you get:

15-20i+6i-8i^2 [combine like terms]

15-14i-8i^2 [but we're not done... the i^2 is not reduced. Because i = sqrt -1, it's really (sqrt -1)^2. But anything sqrt and squared just equals what's in the sqrt, so...]

15-14i-8(-1) [still not done, though. Multiply -8 by -1 = +8]

15-14i+8 [again, combine like terms]

23-14i [final answer]

Hope this helps!

so all you have to do for the first step is use FOIL (first, outside, inside, last) so:

15 - 20i + 6i - 8i^2

then combine any like terms:

15 - 14i - 8i^2

and lastly, rearrange this answer so that the highest power (8i^2) is first and the lowest power (the constant, 15, in this case) is last:

-8i^2 - 14i + 15

another way to solve this would be using distributive property : 5(3-4i) + 2i(3-4i) and then combining like terms and all, but using FOIL would be simplest, in my opinion

hope this helped!!!

Use the F.O.I.L. method.

F.O.I.L. = First Outside Inside Last

First = 5 * 3

Outside = 5 * (-4i)

Inside = 2i * 3

Last = 2I * (-4i)

(5+2i)(3-4i) = 15 - 20i + 6i - 8i^2 = 15 - 14i - 8i^2 or -8i^2 - 14i +15

= 15 - 14i - 8i^2

i^2 = -1

= 15 - 14i + 8

= 23 - 14i

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use the FOIL method:

5x3=15, 5x-4i=-20i, 2ix3=6i, 2ix4i=-8i

15-20i+6i-8i=

15-6i

you would use the process of foiling for that FOIL is First Outer Inner Last and you will get your answer.

Stop asking questions on here which is cheating and Do your homework!! The only way to get better is for you to do it yourself.

Hint: use FOIL

15-14i-8i^2