Question

1. in the complex number system, which of the following is equivalent to (3 - 2i)^2?

○ 9 + 4i
○ 6 - 4i
○ 13 - 12i
○ 5 - 12i

Explanation:

Step1: Expand \((3 - 2i)^2\) using \((a - b)^2=a^{2}-2ab + b^{2}\)

\((3 - 2i)^2=3^{2}-2\times3\times2i+(2i)^{2}\)
\(=9-12i + 4i^{2}\)

Step2: Recall that \(i^{2}=-1\)

Substitute \(i^{2}=-1\) into the above - expression:
\(9-12i + 4\times(-1)=9-12i-4\)

Step3: Combine like - terms

\(9-4-12i=5 - 12i\)

Answer:

\(5 - 12i\)