What are imaginary numbers and how are they used in real life situations?

Answer 1

Imaginary numbers are a mathematical concept, first defined to handle the square root of negative numbers. At first, many mathematicians did not think very kindly of them, until Euler's formula in the 1700's, then later applications in electricity and wave analysis were recognized.

Complex numbers are numbers on a plane, for which special which special operations are defined. Complex numbers have a real part, and an imaginary part.

There are several practical applications; for example, electrical engineers use complex numbers for circuit calculations with AC. There are other applications, too; for example, in art (creating interesting patterns, called fractals - based on calculations with complex numbers). Quantum mechanics routinely uses complex numbers.

The Wikipedia article on complex numbers gives a good overview.

The Picomonster website has some cool animations which show complex and imaginary numbers 'in action', so to speak.