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Concept of Complex Number

  1. Apr 16, 2010 #1

    My question is about Complex number.
    I can solve and calculate complex numbers. But i m still Unsure about the Concept of Complex number.
    I have read many articles and they say that a symbol i is added to make the solutions possible.\

    In communication engineering, as well as Electrical engineering, this number plays an important role.

    Keeping this in mind, Tell me what does the real part and imaginary part of a Complex number shows with an example..Take capacitor or Inductor.
    We have learned in primary classes about the Numbers with Fundamental Concepts.
    Tell me the Fundamental Idea and Concept of Complex number in context to any application or Example so that the idea behind the number can be visualized properly.

    We talk a lot about impedance in transmission lines and they all are in complex number,even in Electrical Machines, Transformer or Motors, I dont understand where actually the real and imaginary part lie??? What does the Real part in practical as well as the imaginary part shows??
    Can you Evaluate or Mark and show me from some observation ( or from graph ,a point ) practically and name it complex number with real and imaginory?

    Saying so , Please share links,Flash Demonstration, so that i can easily understand this number fundamentally!

    And why the real part and imaginoary part are added?? to combine a new number,? and how?
    And since symbol "i" is imaginary , how one can translate the word imaginary?Even knowing the complex number hold a significant value in engineering?Does "i" have some transformation?

  2. jcsd
  3. Apr 16, 2010 #2
    In EE complex numbers are convenient for doing ordinary algebra to solve two-component problems.

    Analyzing circuits at a frequency S turns the differential equations of a circuit into algebraic ones. Laplace transform for example.

    A complex number has a magnitude and a phase. A real number only has a magnitude so it's not easy to solve frequency-domain problems (where every system changes the amplitude and phase of the input but is still sinusoudal.)
  4. Apr 17, 2010 #3
    Think of a number. Say, 150. What can you do with it? Not much! It's bigger than 149. Yawn.

    Now if you wanted to convey information about the weight of your mother, simply saying "150" would be meaningless. 150 what? Tonnes? LOL, of course not -- you meant 150 kg, and that calls for a scalar quantity, which is simply the product of a numerical value and a physical unit.

    But what about the situation where your mother is in free-fall after a parachute jump from a high-altitude balloon? How can we talk about the force that is acting on her body? Well, from the sound of her screaming, we know she's accelerating, and Newton's Second Law or whatever tells us Force = (mass * acceleration). But in what direction is she accelerating? Is she going up? Hell, no. She's going down. So the Force has a magnitude of m*a (measured in kg*m/s^2) and a downward direction. The Force is a vector!

    Notice how we went from a simple number to a scalar, and finally to a vector, and how we were able to increase the amount of information along the way. A complex number is also a vector with a magnitude and a direction (or "phase angle") as any other vector. In the same way that the force vector allowed you to describe your mom in free-fall, complex numbers makes your life easier by, e.g., giving you a way to describe the how the phase of a electrical signal varies with time, etc.
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