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Since complex numbers can be expressed as magnitude and angle, a plot of a system's response can be approximated with a Bode plot (see related link). The gain is the magnitude, and the phase shift is the angle change of the system.

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Q: How complex numbers are used in determining gain of a system?
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What are the applications of complex numbers?

There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?


If you divide 4 by the square root of -7 and then times that by the square root of sin30 how many swag points will you gain?

I am not sure what you want to calculate; anyway, the square root of a negative number is a complex number: in this case, "i" multiplied by the square root of 7. The remaining calculations will also result in complex numbers. When you calculate points, you usually want a real number, not a complex number.


Why do we have negative numbers?

We have negative numbers, because if there were no negative numbers, people wouldn't lose profit, they would always gain.


When you subtract a negative from a positive is that a gain or loss?

When you subtract a negative number from a positive number, it is equivalent to adding the two numbers together. Therefore, it is a gain.


What is difference between transfer function and gain?

Gain is also taken as Laplace transform of output to Laplace transform of Input . for example voltage gain calculation , it is not necessary to make the energy will be zero in L and C ( if present in the given circuit). But in case of Transfer function to avoid the system dynamics , we have to make the inductor and capacitor energy will be zero as initial condition = 0

Related questions

What are the applications of complex numbers?

There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?There are numerous applications; you should read the Wikipedia article on complex numbers for more examples. Some applications include: Get a better understanding of math. Even if you do calculations with real numbers, working with complex numbers often gives a greater understanding.Electricity, with AC, uses complex quantitites.Quantum physicsArt - ever seen the Mandelbrot set, or other fractals?


What is a weight gain calculator most useful for?

A weight gain calculator is useful in determining how many calories you need to intake on a daily basis in order to gain "good" weight and build muscle.


Why do ecologists make models of ecosytems?

to gain insight into its complex phenomena


Steady state gain of the system?

Steady state gain,


If you divide 4 by the square root of -7 and then times that by the square root of sin30 how many swag points will you gain?

I am not sure what you want to calculate; anyway, the square root of a negative number is a complex number: in this case, "i" multiplied by the square root of 7. The remaining calculations will also result in complex numbers. When you calculate points, you usually want a real number, not a complex number.


What does not gain or lose mass?

a closed system will not gain or lose mass


What real numbers represent a gain of 6kg in weight?

A gain of 6 kg in weight


If the gain of the open loop system is doubled then gain margin will become?

gain margin becomes half


Why do we have negative numbers?

We have negative numbers, because if there were no negative numbers, people wouldn't lose profit, they would always gain.


Can Vitamin b complex cause weight gain?

I started taking Vitamin B complex...after 2 weeks I have gained 5 Lbs. Not good. I am stopping it today.


Why gain bandwidth product is constant?

The gain and bandwidth product is constant only for first order systems. However many complex systems which can be converted and studied as first order, it holds good. This is simple mathematics as in the first order system the frequency appears in the denominator. So if it increases by x times then gain (the modulus of the transfer function) is reduced by x times (approximately).


When you subtract a negative from a positive is that a gain or loss?

When you subtract a negative number from a positive number, it is equivalent to adding the two numbers together. Therefore, it is a gain.