To solve the expression $(-3 + 0.6j)(0.4j - 7)$, we can use the distributive property (also known as the FOIL method for binomials). Let's break it down step by step using a table for clarity.

We’ll set up the table for the distribution process:

Term	$-3$	$0.6j$
$0.4j$	$(-3)(0.4j) = -1.2j$	$(0.6j)(0.4j) = 0.24j^2$
$-7$	$(-3)(-7) = 21$	$(0.6j)(-7) = -4.2j$

Now, let's compute the result:

• The first row: $-1.2j + 0.24j^2$
• The second row: $21 - 4.2j$

Putting it all together: $(-3 + 0.6j)(0.4j - 7) = 21 - 4.2j - 1.2j + 0.24j^2$ Simplify the imaginary terms: $= 21 - 5.4j + 0.24j^2$

Since $j^2 = -1$, substitute $0.24j^2 = 0.24(-1) = -0.24$: $= 21 - 5.4j - 0.24$

Finally, combine the real terms: $= 20.76 - 5.4j$

Thus, the product is: $\boxed{20.76 - 5.4j}$

Let me know if you'd like more details or have any questions about the steps!

Here are some related questions to explore:

1. How can the distributive property be applied to more complex expressions?
2. What is the significance of $j^2 = -1$ in complex number operations?
3. How do you handle higher powers of $j$ (like $j^3, j^4$) in multiplication?
4. What are other ways to visualize the multiplication of complex numbers?
5. How do you solve equations involving complex numbers?

Tip: When multiplying complex numbers, always remember to use $j^2 = -1$ to simplify expressions with imaginary terms!