By applying operations for <em>complex</em> numbers, we have these:
- - 5 · x + y = - 8 - i 41
- - x · y = - 29 - i 53
- x · 2 · y = 58 + i 106
- 2 · x - 3 · y = - 15 + i 19
<h3>How to find four equivalent complex expressions</h3>
Herein we must apply the operations of summing two <em>complex</em> numbers, multiplying two <em>complex</em> numbers and multiplying a <em>complex</em> number by a <em>real</em> 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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