Question

simplify.
(6 - 8i)²
write your answer in the form a + bi.

Explanation:

Step1: Apply the square formula \((a - b)^2 = a^2 - 2ab + b^2\)

Here \(a = 6\) and \(b = 8i\), so \((6 - 8i)^2 = 6^2 - 2\times6\times8i + (8i)^2\)

Step2: Calculate each term

• \(6^2 = 36\)
• \(2\times6\times8i = 96i\)
• \((8i)^2 = 64i^2\), and since \(i^2 = -1\), \(64i^2 = 64\times(-1) = -64\)

Step3: Combine the terms

\(36 - 96i - 64 = (36 - 64) - 96i = -28 - 96i\)

Answer:

\(-28 - 96i\)