Final answer:
After performing the complex number calculations, each expression equates to: -x.y equals -29 - 53i matching with (4), 2x - 3y equals -15 + 19i corresponding to (2), -5x + y does not match any given tile, and x·2y equals 58 + 106i matching with (1).
Step-by-step explanation:
The student is asked to match complex number expressions with their equivalent calculations. The values for x are 3 + 8i and for y are 7 - i.
For the expression -x.y, you calculate the negative of x times y:
-(3 + 8i)×(7 - i) = -1×(21 - 3i + 56i - 8i²) = -1×(21 + 53i - 8×(-1)) = -1×(21 + 53i + 8) = -29 - 53i, so this matches with (4).
For 2x - 3y, you calculate two times x minus three times y:
2×(3 + 8i) - 3×(7 - i) = (6 + 16i) - (21 - 3i) = 6 + 16i - 21 + 3i = -15 + 19i, which corresponds to (2).
The expression -5x + y results in negative five times x plus y:
-5×(3 + 8i) + (7 - i) = (-15 - 40i) + (7 - i) = -15 - 40i + 7 - i = -8 - 41i. This does not match with any of the tiles provided.
Finally, x·2y yields x times two y:
(3 + 8i)×(2×(7 - i)) = (3 + 8i)×(14 - 2i) = 42 - 6i + 112i - 16i² = 42 + 106i - 16×(-1) = 58 + 106i, matching with (1).