Question

Describe and correct the error in performing the operation of complex numbers and write the answer in standard form.

Answer 1

Answer:

-20+48i

Explanation:

The solution erroneously began by expressing the square as the square of each of the terms.

$(4+6i)^2=(4)^2+(6i)^2^{}$

However, the correct way is to take the square of the entire expression inside the bracket as shown below:

$(4+6i)^2=(4+6i)(4+6i)$

Next, we expand and simplify our result below:

$\begin{gathered} =4(4+6i)+6i(4+6i) \\ =16+24i+24i+36i^2 \\ =16+48i+36(-1) \\ =16-36+48i \\ =-20+48i \end{gathered}$

The result of the operation in standard form is -20+48i.