What is the polar complex form of a wave with amplitude and phase?

In summary, to find the amplitude and phase of the complex function f(t) = (1-2i)e^(iwt), we can rewrite 1-2i as A\exp(i B) and then combine it with the exponential term to get √5 [cos ((11 ⋅ pi / 12) + wt)] + i √5 [sin ((11 ⋅ pi / 12) + wt)]. The amplitude is √5 and the phase is (11 ⋅ pi / 12) + wt.
  • #1
desklamp2
1
0

Homework Statement


What is the amplitude and phase of the complex function?

f(t) = (1-2i)e^(iwt)

Homework Equations


None/unknown
Normal Polar Form = Real*e^imaginary
i = e^pi/2*i

The Attempt at a Solution



[/B]I am trying to bring this into a normal polar form to easily see the phase and amplitude.

I have got e^iwt - 2e^i(wt+pi/2)

But now I do not know how to combine these two expressions to make 1 wave?
 
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  • #2
Try to rewrite [tex]1-2i[/tex] as [tex]A\exp(i B)[/tex]
 
  • #3
1 - 2i = √5 [cos (11 ⋅ pi / 12) + i sin (11 ⋅ pi / 12)] = √5 e^[i(11 ⋅ pi / 12)]

f(t) = (1-2i) [e^(iwt)]

f(t) = √5 e^[i(11 ⋅ pi / 12)] [e^(iwt)]

f(t) = √5 e^i[11 ⋅ pi / 12 + wt]

f(t) = √5 [cos ((11 ⋅ pi / 12) + wt)] + i √5 [sin ((11 ⋅ pi / 12) + wt)]

Re[f(t)] = √5 [cos ((11 ⋅ pi / 12) + wt)]

Amplitude: √5

Phase: (11 ⋅ pi / 12) + wt

----------------------
Örsan Yüksek
 
Last edited:

What are polar complex form waves?

Polar complex form waves are a type of wave that can be described using polar coordinates, which involve a magnitude and a phase. They are often used to describe electromagnetic waves, such as light or radio waves.

How are polar complex form waves different from other types of waves?

Polar complex form waves are different from other types of waves because they are described using polar coordinates, whereas other types of waves are typically described using Cartesian coordinates. They also have a unique mathematical representation that involves both real and imaginary components.

What is the relationship between polar complex form waves and the complex plane?

Polar complex form waves can be graphically represented on the complex plane, where the magnitude is shown as the distance from the origin and the phase is shown as the angle from the positive real axis. This representation allows for easier visualization and analysis of these waves.

What are some applications of polar complex form waves?

Polar complex form waves have many applications in physics and engineering, including in the fields of optics, electromagnetics, and signal processing. They are also used in mathematical models and simulations to better understand and predict the behavior of various systems.

Are polar complex form waves only found in electromagnetic waves?

No, polar complex form waves can also be found in other types of waves, such as acoustic waves and water waves. However, they are most commonly associated with electromagnetic waves due to their use in describing the behavior of light and other forms of electromagnetic radiation.

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