Write the expression in the standard form a plus bi.

(-12+i)(-12-i)

To write the expression \((-12 + i)(-12 - i)\) in standard form \(a + bi\), we need to expand and simplify the product.

### Step 1: Apply the difference of squares formula
\[
(a + b)(a - b) = a^2 - b^2
\]
Here, \(a = -12\) and \(b = i\).

### Step 2: Substitute into the formula
\[
(-12 + i)(-12 - i) = (-12)^2 - (i)^2
\]

### Step 3: Calculate the squares
\[
(-12)^2 = 144 \quad \text{and} \quad i^2 = -1
\]

### Step 4: Substitute the values
\[
(-12 + i)(-12 - i) = 144 - (-1)
\]

### Step 5: Simplify
\[
144 + 1 = 145
\]

Thus, the expression in standard form is:
\[
145 + 0i
\]

The answer is \(145\).

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

Here are 5 related questions you might find helpful:
1. How do you multiply complex numbers in general?
2. What are the properties of imaginary and complex numbers?
3. How is the difference of squares used in complex number multiplication?
4. What happens when you multiply a complex number by its conjugate?
5. How do you simplify powers of \(i\)?

**Tip**: Remember, multiplying a complex number by its conjugate always gives a real number!

Write the expression in the standard form a plus bi. (-12 + i)(-12 - i)

Discover how to write the expression (-12 + i)(-12 - i) in standard form using the difference of squares formula. This solution explains complex number multiplication and how the product of a complex number and its conjugate results in a real number. Perfect for students in Grades 9-11.

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