Question

drag the tiles to the correct boxes to complete the pairs.
given that x = 3 + 8i and y = 7 - i, match the equivalent expressions.

-5x + y

x · 2y

2x - 3y

-x · y

reset next

Explanation:

Step1: Calculate \(-5x + y\)

Substitute \(x = 3 + 8i\) and \(y = 7 - i\) into \(-5x + y\):

$$
LATEXBLOCK0
$$

Step2: Calculate \(x\cdot2y\)

First, find \(2y = 2(7 - i)=14 - 2i\). Then multiply by \(x\):

$$
LATEXBLOCK1
$$

Step3: Calculate \(2x - 3y\)

Substitute \(x = 3 + 8i\) and \(y = 7 - i\):

$$
LATEXBLOCK2
$$

Step4: Calculate \(-x\cdot y\)

Multiply \(x\) and \(y\) first:

$$
LATEXBLOCK3
$$

Then take the negative: \(-(29 + 53i)=-29 - 53i\)

Now, we need to match these results with the given tiles (assuming the tiles are \(-8 - 41i\), \(58 + 106i\), \(-15 + 19i\), \(-29 - 53i\)):

• \(-5x + y\) matches \(-8 - 41i\)
• \(x\cdot2y\) matches \(58 + 106i\)
• \(2x - 3y\) matches \(-15 + 19i\)
• \(-x\cdot y\) matches \(-29 - 53i\)

Answer:

• \(-5x + y\) → \(-8 - 41i\)
• \(x\cdot2y\) → \(58 + 106i\)
• \(2x - 3y\) → \(-15 + 19i\)
• \(-x\cdot y\) → \(-29 - 53i\)