Find the product and write the result in standard form.

(Simplify your answer. Type your answer in the form

Ask by Wright Schofield. in the United States

Jan 27,2025

Question

Find the product and write the result in standard form. $$ (8-2 i)(-3-6 i) $$ $$ (8-2 i)(-3-6 i)=\square $$ (Simplify your answer. Type your answer in the form $$ a+b i $$

UpStudy AI · Accepted Answer

To find the product of the complex numbers $$ (8 - 2i) $$ and $$ (-3 - 6i) $$ and express it in the standard form $$ a + bi $$, follow these steps:

1. **Multiply the Two Complex Numbers:**
   $$
   (8 - 2i)(-3 - 6i)
   $$
   Apply the distributive property (FOIL method):
   $$
   = 8 \times (-3) + 8 \times (-6i) + (-2i) \times (-3) + (-2i) \times (-6i)
   $$
   $$
   = -24 - 48i + 6i + 12i^2
   $$

2. **Simplify the Expression:**
   Recall that $$ i^2 = -1 $$:
   $$
   = -24 - 48i + 6i + 12(-1)
   $$
   $$
   = -24 - 48i + 6i - 12
   $$

3. **Combine Like Terms:**
   - **Real Parts:** $$ -24 - 12 = -36 $$
   - **Imaginary Parts:** $$ -48i + 6i = -42i $$
   
   So, the expression simplifies to:
   $$
   -36 - 42i
   $$

**Final Answer:**
$$
(8 - 2i)(-3 - 6i) = -36 - 42i
$$
$$ (8 - 2i)(-3 - 6i) = -36 - 42i $$

Find the product and write the result in standard form.

(Simplify your answer. Type your answer in the form

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Find the product and write the result in standard form. (Simplify your answer. Type your answer in the form