Question

Factor the expression with complex numbers: x² + 4.

a) (x + 2i)(x - 2i)
b) (x + 4i)(x - 4i)
c) (x + 2)(x - 2)
d) (x + 4)(x - 4)

Answer 1

To factor the expression x² + 4 with complex numbers, we can use the difference of squares formula. This formula states that if we have an expression of the form a² - b², it can be factored as (a + b)(a - b). In this case, the expression x² + 4 can be rewritten as x² - (-4)². Using the difference of squares formula, we get (x + 2i)(x - 2i). Therefore, the correct answer is a) (x + 2i)(x - 2i).

Step-by-step explanation:

To factor the expression x² + 4 with complex numbers, we can use the difference of squares formula. This formula states that if we have an expression of the form a² - b², it can be factored as (a + b)(a - b). In this case, the expression x² + 4 can be rewritten as x² - (-4)². Using the difference of squares formula, we get (x + 2i)(x - 2i). Therefore, the correct answer is a) (x + 2i)(x - 2i).