Application of imaginary numbers in real life?

What Are Imaginary Numbers?

 An imaginary number is the square root of a negative number and does not have a tangible value.usually the square root of −1, represented by i or j.

  Application of imaginary numbers

 1.complex numbers have a remarkable application in triangular geometry. There is a fascinating theorem called “Marden’s theorem”. I read about this theorem in an article written by Dan Kalman, a doctor of mathematics who works in the Department of Mathematics and Statistics at American University. He claims that this theorem is “the Most Marvelous Theorem in Mathematics.”

2.In electrical engineering alternating currents can be a pain to analyze sometimes. After all, they have voltages that exhibit sinusoidal behavior. With the use of phasors, one can analyze aspects of AC circuits more easily. Analysis of resistors, capacitors, and inductors can be combined into a single complex number, which is called the impedance. Phasors are comparatively easy to interpret, so it’s a lot easier to study AC circuits when studying them in the complex plane! In addition to AC circuits, complex numbers are similarly useful when studying electromagnetic fields, where the quantities of electric and magnetic field strength are combined into a single complex number. 

3.The last application I wish to bring up involves the usage of imaginary numbers to solve integration problems. As it turns out, we can use the aforementioned Euler’s formula to simplify real integration problems and help us find real answers. This is done by using a base integral that has a complex solution. An example of a base integral would be∫ e^(1+i)xdx. Using simple u substitution, we can find the answer to this integral, which is ((1-i)/2)e^(1+i)x + c1 + ic2. With this known imaginary answer, we can compute the answer to a real integral.