## anonymous one year ago (2+sqrt-16)(4-sqrt-9) Do the expression and express the answer in a+bi form.

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1. anonymous

could you draw this one out please?

2. anonymous

$(2+\sqrt{-16})(4-\sqrt{-9})$

3. anonymous

ok thank you

4. SolomonZelman

$$\large\color{black}{ \displaystyle \left(2+\sqrt{-16}\right) \left(4-\sqrt{-9}\right) }$$ you know that: $$\sqrt{-a^2}=\sqrt{a^2}\times\sqrt{-1}=ia$$ And this way, it follows that: $$\bullet~~~~~~\sqrt{-9}=3i$$ $$\bullet~~~~~~\sqrt{-16}=4i$$

5. SolomonZelman

So, you can re-write your expression is: $$\large\color{black}{ \displaystyle \left(2+4i\right) \left(4-3i\right) }$$ then, expand the expression: $$\large\color{black}{ \displaystyle 2\left(4-3i\right)+4i\left(4-3i\right) }$$ continue expanding, and tell me what you get:

6. anonymous

Before I continue, why did you put a 2 and 4i in front of the binomials?

7. SolomonZelman

Have you expanded expressions like: (A+B)(C+D) previously?

8. SolomonZelman

((You would multiply times A times C+D, and B times C+D. Then you add the results.))

9. anonymous

yes but I don't understand how you did that

10. anonymous

Oh!

11. SolomonZelman

Yes?

12. SolomonZelman

So can you continue from: $$\large\color{black}{ \displaystyle 2\left(4-3i\right)+4i\left(4-3i\right) }$$ for me please?

13. anonymous

Yes Im working it out now

14. anonymous

I got a trinomial?

15. SolomonZelman

i is not a variable, it is a square root of -1. And it abides by the property: $$i^2=\left(\sqrt{-1}\right)^2=-1$$

16. SolomonZelman

So the term of i² is just a negative one.

17. SolomonZelman

Anyway, can you post what you have got?

18. anonymous

when I work it out I get 8+22i which isn't the answer

19. SolomonZelman

$$\large\color{black}{ \displaystyle 2\left(4-3i\right)+4i\left(4-3i\right) }$$ $$\large\color{black}{ \displaystyle 2(4)+2(-3i)+4i(4)+4i(-3i) }$$ $$\large\color{black}{ \displaystyle 8+(-6i)+(8i)+(-12i^2) }$$

20. anonymous

4i(4) should be 16i why is it 8i?

21. anonymous

This is where I got my answer wrong

22. SolomonZelman

Oh, sorry, my bad

23. SolomonZelman

yes, you were right.... $$\large\color{black}{ \displaystyle 8+(-6i)+(16i)+(-12i^2) }$$ $$\large\color{black}{ \displaystyle 8+2i+(-12(-1)) }$$ $$\large\color{black}{ \displaystyle 8+10i+(12) }$$ $$\large\color{black}{ \displaystyle 20+10i }$$

24. anonymous

Wow I made a really dumb mistake.. Thanks!

25. SolomonZelman

I did as well.