Question

plify the expression to a + bi form:
$(-8 - 9i)^2$

Explanation:

Step1: Use the formula \((a + b)^2 = a^2 + 2ab + b^2\)

Here, \(a=-8\) and \(b = -9i\), so \((-8 - 9i)^2=(-8)^2+2\times(-8)\times(-9i)+(-9i)^2\)

Step2: Calculate each term

• Calculate \((-8)^2\): \((-8)^2 = 64\)
• Calculate \(2\times(-8)\times(-9i)\): \(2\times(-8)\times(-9i)=144i\)
• Calculate \((-9i)^2\): \((-9i)^2 = 81i^2\), and since \(i^2=-1\), \(81i^2=-81\)

Step3: Combine the terms

\(64 + 144i-81=(64 - 81)+144i=-17 + 144i\)

Answer:

\(-17 + 144i\)