Question

11.) $(-7 + i)^2$

Explanation:

Step1: Apply the square formula

We use the formula \((a + b)^2 = a^2 + 2ab + b^2\), where \(a=-7\) and \(b = i\). So \((-7 + i)^2=(-7)^2+2\times(-7)\times i + i^2\).

Step2: Calculate each term

Calculate \((-7)^2 = 49\), \(2\times(-7)\times i=-14i\), and we know that \(i^2=-1\).

Step3: Combine the terms

Substitute these values back: \(49-14i+(-1)=49 - 1-14i\).

Step4: Simplify the result

Simplify \(49 - 1\) to get \(48\), so the result is \(48-14i\).

Answer:

\(48 - 14i\)