By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
In this question we must derive two complex numbers such that the following conditions are fulfilled:
a² + b² = 5² (1)
c² + d² = 13² (2)
13 · (a + i b) - 5 · (c + i d) = 27 - i 99 (3)
If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):
13 · (4 - i 3) - 5 · (5 + i 12)
52 - i 39 - 25 - i 60
27 - i 99
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
To learn more on complex numbers: https://brainly.com/question/10251853
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