Sure! Let's match the given expressions and their simplified forms step-by-step.
Given:
[tex]\[ x = 4 + 5i \][/tex]
[tex]\[ y = 2 - 9i \][/tex]
The expressions to match are:
1. [tex]\( x \cdot y \)[/tex]
2. [tex]\( 2x \cdot y \)[/tex]
3. [tex]\( -x + 3y \)[/tex]
4. [tex]\( 4x - y \)[/tex]
And the results are:
[tex]\( 53 - 26i \)[/tex]
[tex]\( 106 - 52i \)[/tex]
[tex]\( 2 - 32i \)[/tex]
[tex]\( 14 + 29i \)[/tex]
Let's match each expression with its result:
1. Calculate [tex]\( x \cdot y \)[/tex]:
We know:
[tex]\[ x \cdot y = 53 - 26i \][/tex]
2. Calculate [tex]\( 2x \cdot y \)[/tex]:
We know:
[tex]\[ 2x \cdot y = 106 - 52i \][/tex]
3. Calculate [tex]\( -x + 3y \)[/tex]:
We know:
[tex]\[ -x + 3y = 2 - 32i \][/tex]
4. Calculate [tex]\( 4x - y \)[/tex]:
We know:
[tex]\[ 4x - y = 14 + 29i \][/tex]
So, matching the expressions with their results:
1. [tex]\( x \cdot y \longrightarrow 53 - 26i \)[/tex]
2. [tex]\( 2x \cdot y \longrightarrow 106 - 52i \)[/tex]
3. [tex]\( -x + 3y \longrightarrow 2 - 32i \)[/tex]
4. [tex]\( 4x - y \longrightarrow 14 + 29i \)[/tex]
Therefore, here are the completed pairs:
[tex]\[ x \cdot y \longrightarrow 53 - 26i \][/tex]
[tex]\[ 2x \cdot y \longrightarrow 106 - 52i \][/tex]
[tex]\[ -x + 3y \longrightarrow 2 - 32i \][/tex]
[tex]\[ 4x - y \longrightarrow 14 + 29i \][/tex]
