Where would you use imaginary numbers?

Question

I was just curious about where someone would find it necessary to use imaginary numbers -- you know, that concept they teach in high school-level math where 'i' represents the square root of -1. What field needs them? Are they good for any real-life application, or is it just something they teach so that you understand the concept, but you don't really use them for anything?

Answer 1

Imaginary numbers, actually complex numbers, are enormously useful in many areas of engineering. One example is in trigonometry where difficult trigonometric identities become almost trivial to derive. Another is in analyzing circuits. Using imaginary numbers allows Ohm's law to be applied to passive (resistors, capacitors and inductors) AC circuits. Euler's identity allows cubic equations to be solved analytically. Applying the concept of graphical representation of 2-D vectors provides very powerful tools for the solution of 2-D kinematics problems and difficult geometry problems.

I am a research engineer and I use complex numbers all the time in my work. It is by far one of the most useful tools that I have to solve difficult problems.

Answer 2

confident, there's a reason. in particular to be waiting to precise the strategies of equations like x^2 + one million = 0, which has no actual strategies. Equations and formula that bring about imaginary numbers arise generally interior the sciences and engineering. Voltage, present day, and ability, working example, are particularly some the parts which would be expressed in terms of imaginary numbers.

Answer 3

The most common usage of them is when you need to be able to manipulate 2-dimensional vectors. They make vector operations a lot faster and easier than having to keep track of the x and y components seperately.


Doug

Answer 4

I love imaginary numbers, but I'm a mathematics major, I think it depends on what you're going into. I'm going to need it, but you may not.

Answer 5

Well, I haven't used them since I was in College Algebra.

Then again, I'm a theatre major. We only have to know how to subtract, since all of our money goes away! :-)