Question

Factor the expression over the complex numbers. x^2+36

Answer 1

Note that
a² - b² = (a+b)(a-b)
i² = -1 by definition.

We want to factorize x² + 36 = x² + 6².

Consider the expression
x² - (6i)² = x² - (6²)(i²) = x² - 36i² = x² + 36

Because x² - (6i)² = (x + 6i)(x - 6i)
Therefore
x² + 36 = (x + 6i)(x - 6i)

Answer: (x + 6i)(x - 6i)