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- anonymous

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- welshfella

x^2 + 64
this is a like the difference of 2 squares except you have to use the imaginary number i
remember that i^2 = -1
so can you fit the i values in here
x^2 + 64 = ( x + ____)( x - ____)

- anonymous

im not sure sorry

- welshfella

ok what is the square root of 64?

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## More answers

- anonymous

8

- welshfella

ok so expand this and see if it comes back to x^2 + 64
(x + 8i)(x - 8i)

- anonymous

it does

- welshfella

just as in difference of 2 squares the middle terms will cancel out

- anonymous

okayy.... so that is the first one

- anonymous

?

- welshfella

(x + 8i)(x - 8i) = x^2 + 8ix - 8ix -64*-1 = x^2 + 64

- welshfella

16x^2 + 49
handle it in the same way

- welshfella

take square root of 16x^2 and 49

- anonymous

(16x+7)(x+7)?

- welshfella

No - where are the i's???

- anonymous

(16x+7i)(x+7i)?

- welshfella

and you take Square root of 16x^2

- anonymous

dunno

- anonymous

well its 4, but idk what to do with it

- welshfella

it 4x
4x * 4x = 16x^2

- welshfella

put 4x in each bracket

- anonymous

(4x+7i)(4x+7i)?

- welshfella

yes
(16x + 7i)(x - 7i) would not come back to 4x^2 + 64 because the 2 terms in ix would not cancel out

- anonymous

okay i get it

- anonymous

next ones a bit different

- welshfella

Oh no thats not quite right Look at your signs - doddnt forget its like difference of 2 squares

- anonymous

(16x+7i)(x-7i)?

- welshfella

NO its 4x !!!

- welshfella

(4x + 7i)(4x - 7i)

- anonymous

sorry lol i copy and pasted the wron egquation

- anonymous

i wanted to copy then change the signs but i copied the wrong one

- welshfella

dont know why but i can't copy and paste!

- welshfella

weird

- anonymous

Find the product of (x + 9i)^2.
next one

- welshfella

withe the last 3 you just expand the parentheses in the normal way
(x + 9i)(x + 9i)
first multiply the second bracket by x then multiply it by 9i
= x(x + 9i) + 9i(x + 9i)
= x^2 + 9xi + 9xi + ?
can you do the last bit?

- anonymous

ummmm

- welshfella

9i*9i = ?

- anonymous

sorry i really tired today

- anonymous

81i?

- welshfella

81* i^2
and what is i^2 equal to?

- anonymous

-1

- welshfella

so that is 81 * -1 = -81
x^2 + 9xi + 9xi - 81
now just add the 2 middle like terms

- anonymous

18xi

- welshfella

right
giving
x^2 + 18xi - 81

- anonymous

is that it?

- welshfella

Yes
the 4 th one is done in exactly the same way

- anonymous

can u just set it up (expand it) and ill take from their then you check?

- welshfella

(x - 2i)(x - 2i)
= x(x - 2i) - 2i(x - 2i)

- anonymous

x^2-2xi-2xi-2i^2?

- anonymous

um @welshfella

- welshfella

right so up until the last term -2i*-2i is not -2i^2
- * - = + and 2*2 = 4

- anonymous

x^2-2xi-2xi-4i?

- welshfella

so -2i * -2i = ?

- anonymous

4i?

- welshfella

treat i as if it weer an x or a y
x^x = x^2
i* i = ?

- anonymous

4i^2

- welshfella

* tahs x * x = x^2

- welshfella

right + 4 i^2 = ?

- anonymous

what do you mean by equals?

- welshfella

i^2 = -1
so 4i^2 = ?

- anonymous

-4
4-?

- welshfella

-4

- welshfella

important to remember i = sqrt(-1) so i^2 = -1

- anonymous

k

- welshfella

x^2-2xi-2xi-4
= x^2 - 4xi - 4

- anonymous

so is that the answer cause it says to find the product

- welshfella

yes
the last one is more complicated because the last term in the brackets is (3x + 5i)
so you could do the last part (3x + 5i)^2 first then plug it in later

- welshfella

you can do this in the same way as the last 2
(3 + 5i)(3 + 5i)
= 3(3 + 5i) + 5i(3 + 5i)
ok try and do that

- anonymous

9+15i+15i-25

- welshfella

yea good job
and we can simplify it further to
30i - 16

- anonymous

is that the answer to the problem?

- welshfella

No
we have to plug that in to the expansion
(x + (3+5i)(x + (3+5i)
= x(x + (3+5i) + (3 + 5i)(x + (3+5i)
= x^2 +3x + 5xi + 3x + 9 + 15i + 30i -16

- anonymous

then simplify?

- welshfella

yes

- welshfella

hold on - I'm getting tired to thats wrong

- anonymous

oookkkaaayy

- welshfella

x(x + (3+5i) + (3 + 5i)(x + (3+5i)
= x^2 + 3x + 5xi + 3x + 5xi + 30i - 16

- welshfella

thats it now simplify
that was a tricky one

- anonymous

x^2+6x+10xi+30i-16

- anonymous

?

- welshfella

looks good

- anonymous

is that iT?

- welshfella

yea

- anonymous

Thanks thats it for now

- welshfella

good I think I'll take a break lol

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