https://file.aiquickdraw.com/mathbot/file/17304216997540mmmp3i2.jpg

To solve \( (7 + 7i)^2 \) and express the answer in the form \( a + bi \):

### Step 1: Expand using the square formula
Using the formula \( (a + b)^2 = a^2 + 2ab + b^2 \), let \( a = 7 \) and \( b = 7i \):

\[
(7 + 7i)^2 = 7^2 + 2 \cdot 7 \cdot 7i + (7i)^2
\]

### Step 2: Calculate each term
1. **First term**: \( 7^2 = 49 \)
2. **Second term**: \( 2 \cdot 7 \cdot 7i = 98i \)
3. **Third term**: \( (7i)^2 = 49i^2 \)

Since \( i^2 = -1 \), we have:

\[
49i^2 = 49 \cdot (-1) = -49
\]

### Step 3: Combine terms
Substitute back:

\[
(7 + 7i)^2 = 49 + 98i - 49
\]

Now, combine the real parts:

\[
49 - 49 + 98i = 0 + 98i
\]

So, the answer in the form \( a + bi \) is:

\[
0 + 98i \quad \text{or simply} \quad 98i
\]

### Final Answer
\[
(7 + 7i)^2 = 98i
\]

Would you like more details or have any questions?

---

### Related Questions:
1. How do you multiply two complex numbers?
2. What is the significance of the imaginary unit \( i \) in complex numbers?
3. How do you expand \( (a + bi)^n \) for any integer \( n \)?
4. What are the steps to convert a complex number to polar form?
5. How does squaring affect the magnitude and angle of a complex number?

### Tip
When squaring a complex number, always remember to use \( i^2 = -1 \) to simplify the expression.

Multiply. Write your answer in the form a + bi: (7 + 7i)^2.

Learn how to multiply and simplify the complex number expression (7 + 7i)^2. This step-by-step solution covers key algebraic concepts, including complex numbers, the square formula, and the imaginary unit property. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation