Show all work to multiply quantity 2 plus the square root of negative 25 end quantity times quantity 4 minus the square root of negative 100 end quantity

Question

Tyrion · Answer

@snowflake0531

Tyrion · Answer

@itsmehjay

snowflake0531 · Answer

$$am~I~righ t ~ that~this~is~ (2+ \sqrt{-25})(4-\sqrt{-100})$$

Tyrion · Answer

yes

snowflake0531 · Answer

Do you know the FOIL method?
$$(a+b)(c+d) = ac+ad+bc+bd$$

Tyrion · Answer

no maam

snowflake0531 · Answer

Although the second one is minus sqrt-100, you can take it as plus, negative sqrt-100

snowflake0531 · Answer

@tyrion wrote:

no maam

welp, now you know it now

snowflake0531 · Answer

So can you use that method and simplify that ^^^^

snowflake0531 · Answer

Or do you want me to write this out for you?

Tyrion · Answer

i never used the method so idek how to take the numbers and put them in their spot

snowflake0531 · Answer

$$(2+\sqrt(-25))(4+(-\sqrt(-100))$$ $$2(4)+2(-\sqrt{-100}) + (\sqrt{-25})4 + (\sqrt{-25})(-\sqrt{-100})$$ Do you know how to simplify that?

Tyrion · Answer

no lie,,ion kno wat goin on,,this is a pre test question,,we aint learn dis yet

snowflake0531 · Answer

actually wait, I did it hte wrong way shoot shoot shoot

snowflake0531 · Answer

We have to pull out imaginary numbers

do you know what that is?

Tyrion · Answer

not at all

snowflake0531 · Answer

We have
$$(2+\sqrt{-25})(4-\sqrt{-100})$$ 
$$imaginary~number~is~i~and~i~is~ \sqrt-1$$

snowflake0531 · Answer

And because we have that i is sqrt-1
$$(2+i \sqrt25)(4-i \sqrt100)$$

snowflake0531 · Answer

From there, we have $$(2+5i)(4-10i)$$

snowflake0531 · Answer

Do you get it so far?

Tyrion · Answer

yuh

snowflake0531 · Answer

Okay so now we use the FOIL method
$$2(4) + 2(-10i) + 5i(4) + (5i)(-10i)$$

snowflake0531 · Answer

This simplifies to$$8-20i+20i+50$$

snowflake0531 · Answer

which then equals $$58$$

Tyrion · Answer

ok,,ima tryna write dis stuff down

snowflake0531 · Answer

Okay well, dm me if you have questions, since right now, I have to go

Tyrion · Answer

ok thnx

snowflake0531 · Answer

yw~

surjithayer · Answer

$$(2+5\iota)(4-10\iota)$$$$=2(2+5\iota)(2-5\iota)$$$$=2[(2)^2-(5\iota)^2]$$$$=2[4-25\iota^2]$$$$=2(4-25(-1))$$
$$=2(4+25)$$
$$=2 \times 29$$
=58

kittybasil · Answer

tyrion wrote:

Show all work to multiply quantity 2 plus the square root of negative 25 end quantity times quantity 4 minus the square root of negative 100 end quantity

Okay, let's first turn the words into numbers. "Quantity 2" = 2 "square root of negative 25" = $\sqrt{-25}$ Note: Look at the negative in there. This means you will have an imaginary number "$i$" because $i=\sqrt{-1}$) "times quantity 4" means multiply by 4, or $\times4$ "minus the square root of negative 100" = $\sqrt{-100}$ Note: again, this will have an imaginary number because it has a negative inside the square root. You will notice I mentioned imaginary numbers twice. This only happens when you have negatives inside a square root. What you need to do to resolve that negative is isolate/remove it from the rest of the numbers inside the square root. Here is a step by step example:$$\sqrt{-x^2}=\sqrt{(-1)(x^2)}$$$$=\sqrt{-1}\cdot\sqrt{x^2}$$$$=i\cdot x$$As previously mentioned, the indicator "$i$" means the square root of NEGATIVE ONE. Not a random negative number. This is why you have to separate out the negative from the rest of the numbers.

kittybasil · Answer

Sorry for the formatting error. I would redo it but that's a lot of work... let me know if you get everything!

Continuing on though, we must put everything together. Your end result should be this:$$(2+\sqrt{-25})(4-\sqrt{-110})$$Normally I'd just leave the next steps up to you. However, since it's your first time working with imaginary numbers, I'll do that work to save you some time:$$(2+i\sqrt{25})(4-i\sqrt{110})$$Now the negative square root part has been resolved. Where should we go from here? Share your thoughts @tyrion