Chockletteeidn
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Given that [tex] x = 3 + 8i [/tex] and [tex] y = 7 - i [/tex], match the equivalent expressions.

[tex] 58 + 106i \quad -8 - 41i \quad -29 - 53i \quad -15 + 19i [/tex]

[tex] 2x - 3y \longrightarrow \square [/tex]

Sagot :

GinnyAnsweridn
Let's go through the process of solving for [tex]\(2x - 3y\)[/tex] step-by-step, given [tex]\(x = 3 + 8i\)[/tex] and [tex]\(y = 7 - i\)[/tex].

1. Multiply [tex]\(x\)[/tex] by 2:
[tex]\[ 2x = 2 \cdot (3 + 8i) = 6 + 16i \][/tex]

2. Multiply [tex]\(y\)[/tex] by 3:
[tex]\[ 3y = 3 \cdot (7 - i) = 21 - 3i \][/tex]

3. Subtract [tex]\(3y\)[/tex] from [tex]\(2x\)[/tex]:
[tex]\[ 2x - 3y = (6 + 16i) - (21 - 3i) \][/tex]

4. Distribute the subtraction:
[tex]\[ 2x - 3y = (6 - 21) + (16i + 3i) \][/tex]

5. Combine the real and imaginary parts:
[tex]\[ 2x - 3y = -15 + 19i \][/tex]

Therefore, the equivalent expression for [tex]\(2x - 3y\)[/tex] is [tex]\(-15 + 19i\)[/tex]. So,

[tex]\[ 2x - 3y \longrightarrow -15 + 19i \][/tex]
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