Note that
i² = -1 by definition.
Also,
a² - b² = (a+b)(a-b)
Consider the expression
x² - [i√(50)]² = (x + i√50)(x - i√50)
Also,
x² - (i√50)² = x² - i²(√50)²
= x² - (-1)*50
= x² + 50
Note that
√50 = √[(25*2] = √25 * √2 = 5√2.
Therefore
x² + 50 = (x + 5√2 i)(x - 5√2 i)
Answer: [tex](x+5 \sqrt{2} i)(x-5 \sqrt{2} i)[/tex]
