Problem 10 - Algebra and Trigonometry

Question

Find each product and write the result in standard form. $$ -8 i(2 i-7) $$

Step-by-Step Solution

Answer

The product of the expression \(-8i(2i-7)\) when simplified and written in standard form is \(16 - 56i\).

Step 1: Distribute -8i to the terms inside the brackets

First, distribute -8i to each term inside the brackets which results in: \(-8i * 2i\) and \(-8i * -7\).

Step 2: Multiply the imaginary terms and the real terms separately

Doing the multiplication gives us: \(-16i^2\) and \(56i\). Remember, \(i^2 = -1\). Substituting this into the equation simplifies it to: \(16 - 56i\).

Step 3: Write the result in standard form

In standard form, a complex number is written as \(a + bi\) where \(a\) represents the real part and \(bi\) represents the imaginary part. Here, the result, \(16 - 56i\), is already in standard form.