What should be the influence of the imaginary part on a complex number?

In summary, the conversation discusses the influence of the imaginary part on a complex number in a simulation model. The question is whether the behavior of getting the same result with different values for the real and imaginary parts is expected. A follow-up question is asked about the specific type of simulation and input modeling being used. The response mentions that the imaginary part refers to rotation and the real part to the radius of rotation on the complex plane. The conversation then clarifies that the input is the stiffness and damping coefficients of a material and that changing them separately would typically result in different outcomes, but this is not the case in the current simulation.
  • #1
pseudorandom
2
0
Hi,

What should be the influence of the imaginary part on a complex number?

I am asking because I am running a simulation model where the input is a complex number; say z=a+ib
Now the problem is that I get the same result when I put a=0 and give some high value to b, as when I do the vice-versa.

Should this behaviour be expected?

I look forward to a reply. Thank you in advance.
Regards,
Ila
 
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  • #2
I'm no expert, but I'm pretty sure your question is too general to be given a meaningful reply. What sort of simulation is it? What, specifically, is the input modeling? As far as I understand, the imaginary part of a complex number refers to a quantity of rotation around the complex plane, where the real part refers to the radius of said rotation. Though even this description is likely insufficient.
 
  • #3
Hey! Thanks for your reply. The input is the stiffness and damping coefficients of a material. And youre right; the stiffness corresponds to the amplitude and damping to the phase of the resulting vibrations.
I would expect different results if I change the stiffness and the damping of a material separately. But here i get the same result.
 

1. What is the purpose of the imaginary part in a complex number?

The imaginary part in a complex number is used to represent the vertical component of a number on the complex plane. It allows for the representation of both real and non-real numbers, making operations and calculations involving complex numbers more versatile and comprehensive.

2. How does the imaginary part affect the magnitude of a complex number?

The magnitude of a complex number is determined by the distance from the origin on the complex plane. The imaginary part can affect this distance, as it contributes to the overall value of the complex number. Therefore, the imaginary part can influence the magnitude of a complex number.

3. How does the imaginary part affect the angle of a complex number?

The angle, or argument, of a complex number is determined by the inverse tangent of the imaginary part divided by the real part. Therefore, the imaginary part can significantly impact the angle of a complex number, as it is one of the components used in the calculation.

4. Can the imaginary part be negative or zero?

Yes, the imaginary part of a complex number can be negative or zero. A negative imaginary part indicates that the number is located below the horizontal axis on the complex plane, and a zero imaginary part means that the number is a real number.

5. What is the significance of the imaginary unit in complex numbers?

The imaginary unit, denoted by "i", is used to represent the square root of -1 in complex numbers. It is a fundamental component in the creation and manipulation of complex numbers and allows for the representation of non-real numbers on the complex plane.

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