Question

Simplify the following expression using the order of operations and write it in the form of a + bi: ((-8 +6i) + (5+2i)) / (3 - 4i).

Answer 1

Given:

There is an expression given as below

$\frac{\left(\left(-8+6i\right)+(5+2i)\right)}{3-4i}$

Required:

We need to simplify the following expression using order in a+ib

Explanation:

$\begin{gathered} \frac{\left(\left(-8+6i\right)+(5+2i)\right)}{3-4i} \\ \\ \frac{-8+6i+5+2i}{3-4i} \\ \\ \frac{-8+5+i(6+2)}{3-4i} \\ \\ \frac{-3+8i}{3-4i} \end{gathered}$

Now simplify the denominator

$\begin{gathered} \frac{(-3+8i)(3+4i)}{(3-4i)(3+4i)} \\ \\ \frac{-9-12i+24i-32}{9-(-16)} \\ \\ \frac{-41+12i}{25} \\ \\ -\frac{41}{25}+\frac{12}{25}i \end{gathered}$

Final answer:

(-41/25)+(12/25)i