... yeah, how?
Like x^2 - 2x + 2 > 0
Which should factor to (x - 1 - i)(x - 1 + i) > 0
This isn't crittically important since my homework grade doesn't affect my overall grade, but the point of homework in college like that is to learn... any teachers?
inequalities with imaginary numbers
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Slater - Posts: 2671
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It depends on exactly what they're asking here. I suspect that they're only interested in the set of real numbers x such that the inequality holds in which case, the complex solutions are quite immaterial. On the other hand if they're interested in all values of x that satisfy the inequality, you have to define what the inequality means for complex numbers, which is something that is not immediately clear.
Given that they're not specifically stating that the magnitude of the LHS be greater than zero (which would be trivial), I think we can safely decide that the solutions must be all real and that the imaginary component vanishes. In this case, you need to set x=a+b*i, and expand your equation by substituting in your new definition of x. This will give you two equations that you must solve. One will be all real and must be greater than zero, and the second will be all imaginary and must be equal to zero.
Given that they're not specifically stating that the magnitude of the LHS be greater than zero (which would be trivial), I think we can safely decide that the solutions must be all real and that the imaginary component vanishes. In this case, you need to set x=a+b*i, and expand your equation by substituting in your new definition of x. This will give you two equations that you must solve. One will be all real and must be greater than zero, and the second will be all imaginary and must be equal to zero.
The scientific method," Thomas Henry Huxley once wrote, "is nothing but the normal working of the human mind." That is to say, when the mind is working; that is to say further, when it is engaged in corrrecting its mistakes. Taking this point of view, we may conclude that science is not physics, biology, or chemistry—is not even a "subject"—but a moral imperative drawn from a larger narrative whose purpose is to give perspective, balance, and humility to learning.
Neil Postman
(The End of Education)
Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that my ignorance is just as good as your knowledge
Isaac Aasimov
Neil Postman
(The End of Education)
Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that my ignorance is just as good as your knowledge
Isaac Aasimov
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Technomancer - Posts: 2379
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