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The given problem is to multiply \( 5i(3 - 4i) \) and express the result in the form \( a + bi \).

Let's solve it:

### Step 1: Apply the distributive property (distribute \( 5i \)):
\[
5i(3 - 4i) = 5i \cdot 3 + 5i \cdot (-4i)
\]
\[
= 15i - 20i^2
\]

### Step 2: Simplify using the fact that \( i^2 = -1 \):
\[
15i - 20i^2 = 15i - 20(-1)
\]
\[
= 15i + 20
\]

### Step 3: Write in the form \( a + bi \):
\[
= 20 + 15i
\]

Thus, the result is \( 20 + 15i \).

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you multiply two complex numbers?
2. What is the geometric interpretation of multiplying complex numbers?
3. How do you find the conjugate of a complex number?
4. How does \( i^2 = -1 \) affect complex number multiplication?
5. How do you add and subtract complex numbers?

### Tip:
Always remember that \( i^2 = -1 \) when working with complex numbers, as it's a key step in simplifying results!

Multiply 5i(3 - 4i) and simplify the answer in the form a + bi.

Learn how to multiply and simplify the complex number expression 5i(3 - 4i). This example demonstrates the distributive property, handling imaginary units, and simplifying results in the form a + bi. Ideal for Grades 9-11 students.

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