Question

Difference of Squares gives which complex factors for the expression +3?
A. (x+3i)(x-3i)
B. (x-i-√3)(x-i√3)
C. (x+3i)^2(x-3i)²
D. (x+i√3)(x-i√3)

Answer 1

The difference of squares is:

(x+i√3)(x-i√3)

So the correct option is the last one, D.

Which expression gives x^2 + 3?

For a complex number:

$Z = a + b*i$

We define the complex conjugate of Z as:

$Z' = a - b*i$

Such that the product between the complex number and its complex conjugate gives:

$Z*Z' = a^2 + b^2$

Now, of you look at option D, you can see we have the product of a number and its conjugate, then we can write the product and use the above rule to get:

$(x + i\sqrt{3} )*(x - i\sqrt{3} ) = x^2 + (\sqrt{3} )^2 = x^2 + 3$

Which is what we wanted to get, so that is the correct option.

If you want to learn more about complex numbers:

https://brainly.com/question/10662770

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