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

`(\left(\left(-8+6i\right)+(5+2i)\right))/(3-4i)`

Required:

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

Step-by-step explanation:

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

Now simplify the denominator

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

Final answer:

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