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Stels [109]
3 years ago
12

Factor over the complex numbers, if possible: x² + 2xyi - y2 What is the answer?

Mathematics
1 answer:
yanalaym [24]3 years ago
8 0

9514 1404 393

Answer:

  (x +yi)²

Step-by-step explanation:

Comparing the given expression to the square of a binomial, we can determine the given expression to be a square.

  (a +b)² = a² +2ab +b²

Here, we have a=x and b=yi. Then the factorization is ...

  x² +2xyi +(yi)² = (x +yi)²

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B2-4b+4=0 using quadratic forumla
Ivan

Trying to factor by splitting the middle term   

Factoring <span> b2-4b+4</span> 
The first term is, <span> <span>b2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> -4b </span> its coefficient is <span> -4 </span>.
The last term, "the constant", is <span> +4 </span>

Step-1 : Multiply the coefficient of the first term by the constant <span>  1 • 4 = 4</span> 

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is  <span> -4 </span>.
<span><span>     </span></span>

<span><span>-4   +   -1   =   -5</span><span>     -2   +   -2   =   -4   That's it</span></span>


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  -2 
                     <span>b2 - 2b</span> - 2b - 4

Step-4 : Add up the first 2 terms, pulling out like factors :
                    b • (b-2)
              Add up the last 2 terms, pulling out common factors :
                    2 • (b-2)
Step-5 : Add up the four terms of step 4 :
                    (b-2)  •  (b-2)
             Which is the desired factorization

8 0
4 years ago
Read 2 more answers
75% of what number is 200
Lerok [7]
We try to find the number that 75% of it is 200 by set the number that we try to find by A
-> A x 75/100 = 200
-> (A x 75)/100 = 200
-> A x 75 = 200 x 100
-> A x 75 = 20,000
->A = 20,000/75
-> A = 266.6666...
So that the number that 75% of it is 200 : 266.6667


4 0
3 years ago
Read 2 more answers
What is the perimeter of the triangle in the diagram?<br><br><br> a + b + <br> a2 + b2<br> 2(a + b)
inn [45]
Where is the triangle?
7 0
4 years ago
Read 2 more answers
-4n+3&gt;23<br> A. -5<br> B. 5<br> C. -9<br> D. -20<br> E. 20
Pani-rosa [81]
It will be 20 after u subtract
6 0
3 years ago
Is -2.25 - (-3) a positive number
Zielflug [23.3K]

Answer:

Yes it is

Step-by-step explanation:

The answer is 0.75

-2.25-(_3)

_2.25 +3

=0.75

6 0
3 years ago
Read 2 more answers
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