Question

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Answer 1

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 - ____)

Answer 2

im not sure sorry

Answer 3

ok what is the square root of 64?

Answer 4

8

Answer 5

ok so expand this and see if it comes back to x^2 + 64

(x + 8i)(x - 8i)

Answer 6

it does

Answer 7

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

Answer 8

okayy.... so that is the first one

Answer 9

?

Answer 10

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

Answer 11

16x^2 + 49

handle it in the same way

Answer 12

take square root of 16x^2 and 49

Answer 13

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

Answer 14

No - where are the i's???

Answer 15

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

Answer 16

and you take Square root of 16x^2

Answer 17

dunno

Answer 18

well its 4, but idk what to do with it

Answer 19

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

Answer 20

put 4x in each bracket

Answer 21

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

Answer 22

yes

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

Answer 23

okay i get it

Answer 24

next ones a bit different

Answer 25

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

Answer 26

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

Answer 27

NO its 4x !!!

Answer 28

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

Answer 29

sorry lol i copy and pasted the wron egquation

Answer 30

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

Answer 31

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

Answer 32

weird

Answer 33

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

Answer 34

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?

Answer 35

ummmm

Answer 36

9i*9i = ?

Answer 37

sorry i really tired today

Answer 38

81i?

Answer 39

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

Answer 40

-1

Answer 41

so that is 81 * -1 = -81

x^2 + 9xi + 9xi - 81
now just add the 2 middle like terms

Answer 42

18xi

Answer 43

right
giving
x^2 + 18xi - 81

Answer 44

is that it?

Answer 45

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

Answer 46

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

Answer 47

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

Answer 48

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

Answer 49

um @welshfella

Answer 50

right so up until the last term -2i*-2i is not -2i^2

- * - = + and 2*2 = 4

Answer 51

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

Answer 52

so -2i * -2i = ?

Answer 53

4i?

Answer 54

treat i as if it weer an x or a y

x^x = x^2

i* i = ?

Answer 55

4i^2

Answer 56

* tahs x * x = x^2

Answer 57

right + 4 i^2 = ?

Answer 58

what do you mean by equals?

Answer 59

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

Answer 60

-4
4-?

Answer 61

-4

Answer 62

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

Answer 63

k

Answer 64

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

Answer 65

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

Answer 66

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

Answer 67

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

Answer 68

9+15i+15i-25

Answer 69

yea good job

and we can simplify it further to
30i - 16

Answer 70

is that the answer to the problem?

Answer 71

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

Answer 72

then simplify?

Answer 73

yes

Answer 74

hold on - I'm getting tired to thats wrong

Answer 75

oookkkaaayy

Answer 76

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

Answer 77

thats it now simplify

that was a tricky one

Answer 78

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

Answer 79

?

Answer 80

looks good

Answer 81

is that iT?

Answer 82

yea

Answer 83

Thanks thats it for now

Answer 84

good I think I'll take a break lol