Problem 45 Multiply. $$ (-8 i)(-2 i) ... [FREE SOLUTION]

Chapter 10: Problem 45

Multiply. $$ (-8 i)(-2 i) $$

Short Answer

Expert verified

-16

Step by step solution

Multiply the coefficients

First, multiply the numerical coefficients of the terms. Here, multiply $-8$ and $-2$ to get 16. So, $-8 \cdot -2 = 16$.

Multiply the imaginary units

Next, multiply the imaginary units. Recall that $i^2 = -1$. So, when you multiply \i \cdot i\, it equals $i^2$, which is $-1$.

Combine the results

Combine the results of the coefficients and the imaginary units: $16 \cdot -1 = -16$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Imaginary Units

To understand imaginary units, we start with the imaginary number denoted as $i$. Imaginary units are used to represent the square root of negative one, something not possible with real numbers. Let's break this down:

$i = \sqrt{-1}$
An imaginary number is usually written as multiples of $i$

So when you see $i$, know it refers to this special number.

Complex Numbers Multiplication

Multiplying complex numbers means combing both their real and imaginary parts. For this exercise, let's recall that we're multiplying \-8i\ and \-2i\.Our steps:

Multiply the coefficients (the numbers without $i$). \-8 \-2 = 16
Next, multiply the imaginary units. Remember $i \cdot i = i^2$

After completing each step, we then combine the results. This leads to $16 \cdot i^2$. Since $i^2 = -1$, the equation becomes $16 \cdot (-1) = -16$.

i squared equals negative one

One fundamental idea is that $i^2 = -1$. Here's why:

If $i = \sqrt{-1}$, then squaring both sides, we get $i^2 = (\root -1)^2 = -1$

We use this in our multiplication as well. When multiplying $-8i) \cdot (-2i)$, the term with $i^2$ converts into $-1$. This simplification helps us solve our problem, getting a final result: $-8i \cdot -2i = 16 \cdot -1 = -16$.

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91影视

Multiply. $$ (-8 i)(-2 i) $$

Short Answer

Step by step solution

Multiply the coefficients

Multiply the imaginary units

Combine the results

Key Concepts

Imaginary Units

Complex Numbers Multiplication

i squared equals negative one

One App. One Place for Learning.

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