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Given that [tex]x = 4 + 5i[/tex] and [tex]y = 2 - 9i[/tex], match the equivalent expressions:

- [tex]14 + 29i[/tex]
- [tex]53 - 26i[/tex]
- [tex]2 - 32i[/tex]
- [tex]106 - 52i[/tex]

1. [tex]x \cdot y \longrightarrow \square[/tex]
2. [tex]2x \cdot y \longrightarrow \square[/tex]
3. [tex]-x + 3y \longrightarrow \square[/tex]
4. [tex]4x - y \longrightarrow \square[/tex]

Sagot :

GinnyAnsweridn
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]
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