Question

Given that x = 3 + 8i and y = 7 - i, match the equivalent expressions.

Answer 1

By applying operations for complex numbers, we have these:

1. - 5 · x + y = - 8 - i 41
2. - x · y = - 29 - i 53
3. x · 2 · y = 58 + i 106
4. 2 · x - 3 · y = - 15 + i 19

How to find four equivalent complex expressions

Herein we must apply the operations of summing two complex numbers, multiplying two complex numbers and multiplying a complex number by a real number, which are defined below:

Addition between two complex numbers

(a + i b) + (c + i d) = (a + c) + i (b + d)     (1)

Multiplication between two complex numbers

(a + i · b) · (c + i d) = (a · c - b · d) + i (b · c + a · d)

Multiplication of a complex number by a real number

k · (a + i b) = k · a + i k · b      (2)

Now we proceed to find the equivalent expressions:

- 5 · x + y = - 5 · (3 + i 8) + (7 - i) = (- 15 - i 40) + (7 - i) = - 8 - i 41

- x · y = - (3 + i 8) · (7 - i) = (- 3 - i 8) · (7 - i) = (- 21 - 8) + i (- 56 + 3) = - 29 - i 53

x · 2 · y = (3 + i 8) · 2 · (7 - i) = (3 + i 8) · (14 - i 2) = (42 + 16) + i (112 - 6) = 58 + i 106

2 · x - 3 · y = 2 · (3 + i 8) - 3 · (7 - i) = (6 + i 16) + (- 21 + i 3) = - 15 + i 19

To learn more on complex numbers: brainly.com/question/10251853

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