Question

Write your result in standard form:

3i(4-5i) + 2i(4i-√-25)

Answer 1

which part of this are you stuck on?

Answer 2

I just don't understand where to start.

Answer 3

ok, do you know how to expand each of the bracketed expressions?

Answer 4

I don't :(

Answer 5

ok, lets start from the beginning then. if we have:

a(b+c)

this means "a" multiplied by the sum of "b" and "c". this gives you "a" lots of "b" and "c", so we can expand this as follows:

a(b+c) = ab + ac

do you understand this part?

Answer 6

Yes, I do.

Answer 7

e.g.:

3(4+2) = 3*4 + 3*2 = 12 + 6 = 18

we can this as 4+2=6, so 3(4+2) = 3 * 6 = 18

Answer 8

ok, so lets try to expand the first expression:
\[3i(4-5i) =3i*4 - 3i*5i=12i-15i^2\]now since \(i=\sqrt{-1}\) we know that \(i^2=-1\), we therefore get:\[3i(4-5i)=12i-15i^2=12i-(15*-1)=12i-(-15)=12i+15\]
got that?

Answer 9

yes, i do. the radicals are what confuse me.

Answer 10

ok, so lets look at those nasty radicals next...

Answer 11

in this expression:\[2i(4i-\sqrt{-25})\]the \(\sqrt{-25}\) can be written as follows:\[\sqrt{-25}=\sqrt{25*-1}=\sqrt{25}*\sqrt{-1}=\sqrt{25}*i=5i\]so we can rewrite the original as:\[2i(4i-5i)\]understand so far?

Answer 12

Where did you get the -1? Or do we multiply by that so we can get rid of the negative?

Answer 13

-25 = 25 * -1

Answer 14

any positive number times -1 will give you the negative of that number

Answer 15

Right, I understand that now.

Answer 16

\[2i(4i-\sqrt{-25})=2i(4i-5i)=2i(-i)=2i * -i = -2i^2 = -2 * i^2\]\[= -2 * (-1) = 2\]

Answer 17

does that make sense?

Answer 18

yes.

Answer 19

ok, so finally we put it all together to get:\[12i+15+2=12i+17\]the standard form for a complex number is usually written as:\[a+bi\]where \(i=\sqrt{-1}\) so we can just rearrange the final answer to get:\[17+12i\]

Answer 20

That was a tough one! I'm starting to get the hang of this radical stuff. Thank you so much.

Answer 21

yw - I'm glad I could help you understand.

Answer 22

I'm terrible at this math stuff. I'm glad there are people like you that can help break it down.

Answer 23

have faith in your abilities and you will achieve things you never thought you could. :-)

Answer 24

I will surely remember that :)

Answer 25

take care...

Answer 26

you too! Thank you once again.