what is really meaning of module of a complex number?

[hanhan]

Hi, I have seen this in a lecture slide.
The combination of a real and an imaginary term is called a complex number.
Usually, the real number is written first.
As an example, 3 + j4 is a complex number including 3 units on the real axis added to 4 units 90° out of phase on the j axis.


Then I would like to know what is really meaning of module of a complex number?
For example, z = 3 + j4 then moldule of z is 5. What is the meaning of 5 in this case?
For example, in a circuit we have R = 3Ω, ZL = ωL = 4Ω
Then z = 5Ω
Why we call z= 5 is the total impedance of the circuit?
What is it role?
In the figure bellow, why we can attach hypotenuse of the right triangle by 3 + j4, 3- j4, 5 + j2, 5 - j2?

 

[misterT]

It is distance from origin 0 + j0

Different applications of complex numbers give different meanings what the distance from origin means. Using modulus you can compare different complex numbers "which one is further from origin".

Somebody else can explain what impedance means.. I don't have enough time now

The blue hypotenuse is the complex number illustrated the same way vectors are. The red arrows are just the real and complex components of the complex number.

 

[MrAl]

Hi,

I think you mean the 'modulus' right? That's the amplitude, which is the square root of the sum of squares of the two components.

Sometimes Mod means to divide a number by another number and compute the remainder.

 

[hanhan]

Thanks for helps.
Why we don't write z = 5 instead of z = 3 + j4 and we don't need complex number anymore?
And why we need the phase here? In this case I assumes that R = 3 ohm and ZL = 4 ohm.

 

[MrAl]

Hi,

We need both. We need to know z=5 sometimes and we need to know the more complete discription z=3+j4 sometimes.

Complex numbers help to simplify greatly some problems in mathematics and so that means it makes some circuits easier to analyze. This is especially true for AC circuits where the quantities are all AC, and AC quantities can be described very well using complex numbers that's why you see them so much.

We could do a couple examples.

 

[Ratchit]

anhnha,

Then I would like to know what is really meaning of module of a complex number?

You need to read this thread. https://www.electro-tech-online.com/threads/why-dont-imaginary-numbers-make-so-much-sense.121331/

Ratch