Problem 9 - Algebra and Trigonometry

Question

Find each product and write the result in standard form. $$ -3 i(7 i-5) $$

Step-by-Step Solution

Answer

The product is \(-21 + 15i\).

Step 1: Distribute \(-3i\) to both terms in the parentheses

Multiply \(-3i\) with \(7i\) and also with \(-5\). This gives \(-3i * 7i\) and \(-3i * -5\).

Step 2: Calculate the products

Multiplying \(-3i * 7i\) gives \(21i^2\). Remember that \(i^2\) is \(-1\). Multiplying \(-3i * -5\) gives \(15i\). So, now we have \(21(-1) + 15i\).

Step 3: Simplify the result to standard form

Calculating \(21(-1)\) gives \(-21\). Therefore, the product is written in standard form as \(-21 + 15i\)