What are the practical uses of complex numbers, square root of minus 1?

Answer 1

Electrical engineers who deal with power systems use complex numbers. Instead of i, they use j since i is used to designate current.

AC circuits have resistance and reactance. R and X. The sum of these two complex numbers is impedance, Z.

Answer 2

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Answer 3

A complex number is simply a "vector" that needs two numbers to define it. Think of a linear number scale along the x-axis. It has values {...-3,-2, -1, 0, +1, +2, +3, ...} not just the integers, but all values. This is a one dimensional system. Rather boring. Now let's add the y-axis. Now we have an x-y plane and we have two dimensions. Now imagine a point in the plane, rotating around the center point (0,0), at a radius of R, with a constant velocity. To define the exact position of this point, we need to specify both x and y values, or both the real and the imaginary parts. It is a very important fact, that if the point is moving in a circle at constant speed, both the x value and the y value as a function of time are sinuosoids. The exact phase of anything that rotates or vibrates can defined using a complex number. Radio circuits which are tuned, cannot be designed without using complex numbers.

Answer 4

Uses Of Complex Numbers

Answer 5

The practical uses of complex numbers:
1)solving second order differential equations.
2)Complex numbers are needed for the fundamental theorem of algebra: Every polynomial equation, P(x) = 0, with complex coefficients has a complex root. For example, the polynomial equation x2 + 1 = 0 has no real roots. If one allows complex numbers, however, it has two: 0 + i and - i.
3)Complex numbers are also used in the branch of mathematics known as "functions of complex variables." Such functions can often describe physical situations, as in electrical engineering and fluid dynamics, which real-valued functions cannot.

Answer 6

Complex numbers are used heavily by Electrical Engineers in circuit design because they simply the mathematical solving of many types of electronic circuits. They allow sinusoidal steady state circuits to be solved by shifting them from a time domain to a frequency domain, and thus they can be solved with simple algebra rather than messy differential equations. You do lose some information to your solution when shifting domains such as transient response, but many times this information is not of a concern.

Answer 7

Complex numbers are very handy in controls theory and also vector analysis in electronics. Stick with it this stuff does have its uses.

Answer 8

When you realize that there are more than 3 dimensions and time is the 4th, you need the complex part to specify time variation.

Answer 9

They're used in Engineering and Physics all the time.

I use them in trading financial instruments.

For most people, though, they're of no value.

Answer 10

The only practical use I ever found was that it got me from 8th grade, into 9th grade, beyond that, and 40 years have passed, I've yet had a use for that information