Question

perform the indicated operation. write the answer in the form $a + bi$.
$(3 - 2i)^2=square$

Explanation:

Step1: Expand using formula

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

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

Step3: Combine terms

$9-12i-4=(9 - 4)-12i=5-12i$.

Answer:

$5-12i$