(2plus+8i​)(2minus−8i​)equals=enter your response here
​(Type your answer in the form aplus+bii​.)

To solve \((2 + 8i)(2 - 8i)\), we apply the formula for multiplying complex conjugates:

\[
(a + bi)(a - bi) = a^2 - b^2i^2
\]

where \(a = 2\) and \(b = 8\).

Now calculate:

\[
(2 + 8i)(2 - 8i) = 2^2 - (8i)^2
\]

This simplifies to:

\[
= 4 - 64i^2
\]

Since \(i^2 = -1\), we substitute and get:

\[
= 4 - 64(-1) = 4 + 64 = 68
\]

So, the answer is:

\[
68 + 0i
\]

The final answer in the form \(a + bi\) is:

\[
68 + 0i
\]

Would you like any further details or have questions? Here are 5 related questions:

1. How do you multiply two complex numbers?
2. What are complex conjugates, and why are they important?
3. Can you explain how \(i^2 = -1\) affects calculations?
4. How do you express a complex number in polar form?
5. How would the multiplication change if both terms were \(2 + 8i\)?

**Tip:** When multiplying conjugates of complex numbers, the imaginary parts cancel out, leaving a real number.

(2 + 8i)(2 - 8i) = ? (Type your answer in the form a + bi.)

Discover how to multiply complex conjugates using the formula (a + bi)(a - bi) = a^2 - b^2i^2. This example, (2 + 8i)(2 - 8i), simplifies to 68 + 0i. Suitable for students in Grades 9-12 studying complex numbers.

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