Question

lesson: multiplying complex numbers
simplify: (3 - 2i)² (type your final answer in the box. do not put any spaces)

Explanation:

Step1: Apply the square formula

We use the formula \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = 3\) and \(b = 2i\). So \((3 - 2i)^2=3^2-2\times3\times2i+(2i)^2\).

Step2: Calculate each term

Calculate \(3^2 = 9\), \(2\times3\times2i = 12i\), and \((2i)^2 = 4i^2\). Since \(i^2=-1\), then \(4i^2 = 4\times(-1)=-4\).

Step3: Combine the terms

Substitute the values back: \(9 - 12i - 4\). Combine the real parts: \(9 - 4 = 5\). So the result is \(5 - 12i\).

Answer:

\(5-12i\)