Imaginary numbers?

Question

Alright, so, I'm a freshman in college this year, and I'm majoring in math, but I have a question. What applications to real life does an imaginary number have? I've always found reasons for all of the other types of math, even if I don't use them, but imaginary numbers just seem useless and bizzare. Can anyone give me a situation, or even a story problem that can give a possible (even if not likely) situation in which you would need to use an imaginary number?

Answer 1

Imaginary numbers can be used for analyzing the dynamics of a system. The easiest example I know if is in electronics. It is possible to solve simple problems with inducters (which limit the change in current flow) and resistors (which limit the current flow itself), however, if you wanted to model a continuously changing system, the math gets ugly really fast. So you do a mathematical transform of the problem and it ends up that resistors only affect the real part of the problem, and indctors the imaginary. The same thing goes for capacitors as well. This is very important for electrical systems because if the capacitance and inductance are not properly matched you can actually lose power in the system. This would matter in the real world if you ever designed a gas discharge (like a neon light) because if the attached capacitor is the wrong size the light will actually create a reverse flow of electricity, meaning it takes more power to run. On a graph what this looks like is the voltage and current plots have a phase shift between them (and that is what the imaginary part of the transform measures, the change in phase)

Answer 2

Yes, there is a reason. Mainly to be able to express the solutions of equations like x^2 + 1 = 0, which has no real solutions. Equations and formulas that lead to imaginary numbers come up frequently in the sciences and engineering. Voltage, current, and power, for example, are some of the quantities that can be expressed in terms of imaginary numbers.

Answer 3

i have a b.a. in math and i am almost done with my m.a. too. you really don't see imaginary numbers all that much. i took a whole class about it called "complex analysis." it was pretty interesting and made me more at ease with imaginary numbers. in that class there were a LOT of physicists. every example to life that the teacher gave, they always understood it. i can't remember any at the moment. if you are uneasy about imaginary numbers you should be ok throughout college, unless you were planning to get a master's in physics. hope this helps...

Answer 4

You really cannot appreciate the usefulness of imaginary numbers until you get into higher mathematics. Euler's equation connects several important numbers in the equation
e^i*pi = -1. In trigonometry, you learned about cis theta which is = cos theta + i sin theta and how De Moivre's theorem can be used to raise complex numbers to any power including any root.

Answer 5

1. Complex arithmetic. Imaginary numbers make up part of the complex plane.
2. Electrons, i is called the j-operator in AC phases.

Answer 6

Imaginary/complex numbers are used extensively when dealing with sinusoidal functions. Electrical engineers use them extensively for modeling a.c. circuits.

Answer 7

no......math is all about doing stuff that u will never do in life