Answer:
25x² + 144 = (5x + 12i) (5x - 12i).
Step-by-step explanation:
We have to factorize the expression 25x² + 144, using the complex number.
Now, [tex]i = \sqrt{- 1}[/tex] can be treated as the complex number as there is negative value with in square root.
So, [tex]i^{2} = - 1[/tex]
Therefore, we can write the original expression as
25x² + 144
= 25x² - (i²)(144)
= (5x)² - (12i)²
= (5x + 12i) (5x - 12i)
So, the factorization is 25x² + 144 = (5x + 12i) (5x - 12i). (Answer)
