Question

multiply.
\\((\sqrt{7} + 5i)(\sqrt{7} - 5i)\\)
\\((\sqrt{7} + 5i)(\sqrt{7} - 5i) = \square\\)
(simplify your answer. type an exact answer, using radicals as needed. type your answer in the form \\(a + bi\\).)

Explanation:

Step1: Apply difference of squares

Recall $(a+b)(a-b)=a^2-b^2$. Here $a=\sqrt{7}$, $b=5i$.
$$(\sqrt{7})^2 - (5i)^2$$

Step2: Simplify each squared term

Calculate $\sqrt{7}$ squared and $5i$ squared, use $i^2=-1$.
$$7 - (25i^2) = 7 - (25\times(-1))$$

Step3: Compute final value

Simplify the expression.
$$7 + 25 = 32$$

Answer:

$32 + 0i$ (or simply $32$)