Question

Complete the indicated operation in the form of a +bi(3-4i)^2

Answer 1

Step-by-step explanation:

The question is given below as

`(3-4i)^2`

Concept:

Apply the perfect sqaure formula below

`(a-b)^2=(a-b)(a-b)`

By applying the concept, we will have

`\begin{gathered} (3-4\imaginaryI)^2=(3-4i)(3-4i) \\ (3-4i)(3-4i)=3(3-4i)-4i(3-4i) \\ 3(3-4i)-4i(3-4i)=9-12i-12i+16i^2 \\ recall:i^2=-1 \\ 9-12i-12i+16i^2=9-24i+16(-1) \\ 9-16-24i=-7-24i \end{gathered}`

Hence,

The final answer is

`\begin{equation*} -7-24i \end{equation*}`