Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Multiplying Complex Numbers
**Problem Statement:**
Multiply the complex numbers:
\[ (-4 + 5i)(-6 + 6i) \]
Write your answer as a complex number in standard form.
**Solution:**
To multiply these two complex numbers, we use the distributive property (also known as the FOIL method for binomials):
\[ (-4 + 5i)(-6 + 6i) = (-4)(-6) + (-4)(6i) + (5i)(-6) + (5i)(6i) \]
Breaking this down step by step:
1. \((-4)(-6) = 24\)
2. \((-4)(6i) = -24i\)
3. \((5i)(-6) = -30i\)
4. \((5i)(6i) = 30i^2\)
Since \(i^2 = -1\):
\[ 30i^2 = 30(-1) = -30\]
Now, combine all the real and imaginary parts:
\[ 24 - 30 + (-24i - 30i) \]
This simplifies to:
\[ (24 - 30) + (-54i) \]
\[ -6 - 54i \]
**Final Answer:**
\[ -6 - 54i \]
**Instructions:**
Enter your answer as a complex number in standard form in the provided text box.
**Visual Representation:**
On the page, there is a rectangular textbox followed by the "i" symbol indicating where to input the imaginary part of the complex number. Additionally, two small boxes with mathematical symbols can help format the complex number properly.
Would you like more practice on multiplying complex numbers or an explanation of another mathematical concept? Click "Continue" to proceed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d26ccc5-6d07-40ec-9d02-12eee6733871%2F223afa6d-03ca-4b4f-88a1-889ccf73db7c%2Fyu921qij_processed.jpeg&w=3840&q=75)
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