What do you ever use imaginary numbers like i (√-1) for in real life?

Answer 1

Remember, mathematics is a tool, a way to help us humans keep track of nature. We can't keep track of money unless we use math (counting). We can't keep track of how fast we are going unless we use math (calculus).

Similarly, imaginary numbers are very useful in helping scientists and mathematicians keep track of all sorts of things. Many problems involving waves (sound, light, and electrical signals) use imaginary numbers.

In Quantum Mechanics, physicists use imaginary numbers to keep track of certain states (energies) of particles.

Without imaginary numbers we wouldn't be able to mathematically describe many of the modern electrical devices we use today. Lasers, Microchips, LEDs, and transistors.

Answer 2

Other than the electronics already mentioned, they can be used in phase equations in circuits.

Also, you can represent vectors with them and imagine each vector having a real and a non-real component. Then, you can add, subtract, multiply, and divide the vectors and have it mean something.

As for the non-engineering applications, there are coding theories, complex analysis, modern algebra, number theory, and other less applied areas of mathematics that use them extensively.

They can be the answers to some trig problems that would be very hard to do without them. DeMoivre's theorem comes to mind as a way to finding the non-real roots of 1. These can then be used to convert some circular/trig representations into complex number representations.

Answer 3

When you are working an electric circuits problem there is a component of the calculation called the 'reactive' power. To do the problem this part is assigned i or the imaginary numbers. You work out the calculation to find the apparent and the true power of a "power triangle". The reactive or imaginary part of the triangle is the hypoteneuse, while the true and apparent power sides are the adjacent and opposite sides.

Answer 4

In everyday real life you don't use them much.
But these numbers are the backbone of much
of scientific and engineering theories. Many
great innovations of our time would not exist
without them.
For example, Steinmetz used complex numbers
to work out the theory for alternating current.

Answer 5

It is used in computations in electric power delivery, and electric motors and generators.

Answer 6

When your kids (when you have some) need help with their homework.

Answer 7

Imagine there's no heaven ..... (Lennon)

Answer 8

you don't, unless you're a mathematician.