Question

write the product (4 + i)(4 - i) in the form a + bi. a. 16 - i b. 16 - i² c. 17 d. 8

Explanation:

Step1: Apply difference of squares

The expression \((4 + i)(4 - i)\) is a difference of squares, which follows the formula \((a + b)(a - b)=a^2 - b^2\). Here, \(a = 4\) and \(b = i\), so we get \(4^2 - i^2\).

Step2: Simplify using \(i^2=-1\)

We know that \(i^2=-1\), so substitute that into the expression: \(16-(-1)\).

Step3: Calculate the result

Simplify \(16 - (-1)\) to \(16 + 1=17\), which is in the form \(a+bi\) with \(a = 17\) and \(b = 0\).

Answer:

C. 17