ALGEBRA!!
Factor completely over the complex numbers.
x^4+18x^2+81
Any idea how the final answer looked like?
(x^2+9)(x^2+9)

Question

ALGEBRA!!
Factor completely over the complex numbers.
x^4+18x^2+81
Any idea how the final answer looked like? 
(x^2+9)(x^2+9)

anonymous · Answer

Guys help! @ganeshie8 @Nnesha @Michele_Laino

anonymous · Answer

@Luigi0210 @sammixboo @welshfella :D

welshfella · Answer

yea that's correct

welshfella · Answer

oh you need  it over complex numbers

anonymous · Answer

Yep maybe (x^2+9i)^2 (x^2+9i)^2 ?

welshfella · Answer

fill in the blanks  
x^2 + 9  =   (x      3i)(x     3i)   ?

anonymous · Answer

(x^2+3i)(x^2+3i) ?

welshfella · Answer

what signs go in the parentheses?

anonymous · Answer

Both positives

welshfella · Answer

no and its x not x^2

welshfella · Answer

x^2 + 9  =  (x + 3i)(x - 3i)

anonymous · Answer

Oh i get it

anonymous · Answer

x^4+18x^2+81 this is the that will be factored over the complex numbers

welshfella · Answer

so   complete factors are
(x + 3i)(x - 3i)(x + 3i)(x - 3i))

anonymous · Answer

Is that the same with (x+3i)^2(x-3i)^2 ??

welshfella · Answer

yes you can write it that way

welshfella · Answer

are you happy about multiplying these imaginary numbers?

-3i  * + 3i  = -9 * i^2  = -9 * - 1 = +9


because   i^2  = -1

anonymous · Answer

|dw:1440088856517:dw|

anonymous · Answer

Looks like this?

anonymous · Answer

@welshfella

welshfella · Answer

- where did you get that from?
its not x^2  it is x

welshfella · Answer

If you expanded that the first term would be x^8  not x^4

anonymous · Answer

attachment

welshfella · Answer

thats it

anonymous · Answer

Thanks! :)

welshfella · Answer

yw

anonymous · Answer

Reasons why i love openstudy, and @welshfella Hahahaha

anonymous · Answer

If i can give you 1000 medals I will