Complex analysis for mathematics and engineering pdf

What are complex numbers used for in engineering?
Complex numbers are used by Electrical & Electronic Engineers to define the Alternating Current or AC concept of Impedance, and in Fourier analysis they are used in the processing of radio, telephone and video signals, see this page for more details..
Why do we need complex numbers in engineering?
Mechanical & Structural Engineers use complex numbers to analyse the vibration of structures in machines, buildings and bridges, the behaviour of fluid flow around aircraft, and that of wind around buildings and bridges, preventing failures such as the Tacoma Narrows Bridge (Please watch the following video)..
What is the importance of complex numbers? While their day-to-day application is not as direct as that of real numbers, their imaginary component makes complex numbers important as they make it possible to work very precisely in specific areas of science and physics.
√5 is an irrational but 3√5 is a complex number.
Write the truth values of the following statements : (a) sqrt5 is an If X is the a random variable with probability mass function P(x) = If sec((x+y)/(x-y))=a^(2),"then "(d^(2)y)/(dx^(2))=

What are complex numbers used for in engineering?