Question

Let a = 2i + 3, b= i – 1, and c= -3i + 2. Which expression is equivalent to a -b- c?A. –2i +4B. 4i + 2C. 4i + 4D. -2i + 2

Answer 1

Given:

$\begin{gathered} a=2i+3 \\ b=i-1 \\ c=-3i+2 \end{gathered}$

You know that:

$a-b-c=(2i+3)-(i-1)-(-3i+2)$

In order to solve the operation, you can follow these steps:

1. Distribute the negative signs. Remember the Sign Rules for Multiplication:

$\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ +\cdot-=- \\ -\cdot+=- \end{gathered}$

Then:

$=2i+3-i+1+3i-2$

2. Combine the like terms (add the Real Parts and add the Imaginary Parts):

$=4i+2$

Hence, the answer is: Option B.