Sure, let's match the given expressions with their equivalent results:
Given values:
[tex]\[ x = 3 + 8i \][/tex]
[tex]\[ y = 7 - i \][/tex]
The expressions to evaluate are:
1. [tex]\( -5x + y \)[/tex]
2. [tex]\( 2x - 3y \)[/tex]
3. [tex]\( -x \cdot y \)[/tex]
4. [tex]\( x \cdot 2y \)[/tex]
We'll pair each expression with its corresponding result.
### Step-by-Step Matching
1. Evaluate [tex]\( -5x + y \)[/tex]:
- This is paired with [tex]\( -29 - 53i \)[/tex].
2. Evaluate [tex]\( 2x - 3y \)[/tex]:
- This is paired with [tex]\( -8 - 41i \)[/tex].
3. Evaluate [tex]\( -x \cdot y \)[/tex]:
- This is paired with [tex]\( -15 + 19i \)[/tex].
4. Evaluate [tex]\( x \cdot 2y \)[/tex]:
- This is paired with [tex]\( 58 + 106i \)[/tex].
So, we get the following pairs:
[tex]\[ -5x + y \rightarrow -29 - 53i \][/tex]
[tex]\[ 2x - 3y \rightarrow -8 - 41i \][/tex]
[tex]\[ -x \cdot y \rightarrow -15 + 19i \][/tex]
[tex]\[ x \cdot 2y \rightarrow 58 + 106i \][/tex]
Therefore, the completed pairs are as follows:
1. [tex]\( -5 x + y \quad \xrightarrow{\longrightarrow} \quad -29 - 53i \)[/tex]
2. [tex]\( 2 x - 3 y \quad \xrightarrow{\longrightarrow} \quad -8 - 41i \)[/tex]
3. [tex]\( -x \cdot y \quad \xrightarrow{\longrightarrow} \quad -15 + 19i \)[/tex]
4. [tex]\( x \cdot 2 y \quad \xrightarrow{\longrightarrow} \quad 58 + 106i \)[/tex]
These are the correct matches for the given expressions with their equivalent results.
