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- As with many other topics of advanced math, it depends whether your "real life" includes working in some engineering area, or not. If you work in electrical engineering or electronics, you will use complex numbers on a daily basis; similarly if you do a lot of math for some reason.
- Complex Numbers (ones involving the imaginary unit 'i' which is defined to handle the square root of -1) are a convenient way to describe the behavior of some electric circuits and waves.
- One thing you may encounter in your 'real life' are uninterruptible power supplies (UPS - what keeps your computer running when the power goes out). You will see ratings such as 500 VA / 300 W. This has to do with Complex Power. Electric circuits, which have inductances (such as Transformers and electric motors) or capacitors, behave in a way that is described by complex numbers. While Volts X Amps equals Watts, the 300 W is the 'real power' (the amount available to do work), and the 500 VA is the apparent power (the total power that the power supply is capable of producing). The reactive power (due to capacitance & inductance) is represented by the imaginary component and it is at right angles to the real power (represented by the real component).
- Another use of complex numbers is in the Fast Fourier Transform (FFT) - one of the most ubiquitous algorithms - used heavily for signal processing. If you have a digital camera, a cell phone, an LCD - FFT is there, bringing complex numbers along.
- The complex equation w=z+1/z is a basic formula used for designing air foils-airplane wings and Figuring out flow forces around a circular object in water for instance.
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What is complex math?
Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
What sets of numbers is not a subset of the real numbers?
The complex numbers.
The sum of two complex numbers is always a complex number?
A "complex number" is a number of the form a+bi, where a and b are both real numbers and i is the principal square root of -1. Since b can be equal to 0, you see that the real numbers are a subset of the complex numbers. Similarly, since a can be zero, the imaginary numbers are a subset of the complex numbers. So let's take two complex numbers: a+bi and c+di (where a, b, c, and d are real). We add them together and we get: (a+c) + (b+d)i The sum of two real numbers is always real, so a+c is a real number and b+d is a real number, so the sum of two complex numbers is a complex number. What you may really be wondering is whether the sum of two non-real complex numbers can ever be a real number. The answer is yes: (3+2i) + (5-2i) = 8. In fact, the complex numbers form an algebraic field. The sum, difference, product, and quotient of any two complex numbers (except division by 0) is a complex number (keeping in mind the special case that both real and imaginary numbers are a subset of the complex numbers).
Which of these are complex numbers 5 3i 1 2i?
All of them. Real numbers are a subset of complex numbers.
What are real life applications of real number system?
shopping, travel, measurements and money are the real life applications of real number system.
