Difference between real and complex signals

[MikeSv]

Hello everyone.

Iam trying to get my head around the difference between real and complex numbers, but Iam having a hard time...
I read that the difference is that a complex signal contains phase information.

If I look at a real signal --> x(t) = Acos(wt + Θ)
and compare it with a complex --> x(t) = Acos(wt + Θ) + i Asin(wt + Θ)

I can only see that both the real and the complex signal have phase information...

So what exactly is the difference ?

Thanks in advance for any help,

kind regards,

Mike

 

[anorlunda]

https://www.physicsforums.com/insights/case-learning-complex-math/

We have a PF Insights article that may help you to understand what is different and why complex is useful. Read that first, then post again if you have questions.

 

[MikeSv]

Hi and thank you so much for your reply and the link to the article. I went through it but I still couldn't figure it out.

As I have understood its about the direction (phase).
But what does that mean with respect to a sinusoidal signal.

Is there a difference between then phases in the real and complex notation in my first post?

Thanks again,

Kind regards,

Michael

 

[anorlunda]

If you are only interested in one signal, then it makes no difference which notation you use, (sin, complex, power series, expotential) they are all the same thing.

The advantage of one notation or another comes when you try to do things with it. For example, adding two sinusoidal signals,
$A\sin{(\omega{t}+\theta_A)}+B\sin{(\omega{t}+\theta_B)}=C\sin{(\omega{t}+\theta_C)}$

Using complex, it is very easy to solve for $C$ and $\theta_C$. How would you do that with sin notation?

 

[MikeSv]

If you are only interested in one signal, then it makes no difference which notation you use, (sin, complex, power series, expotential) they are all the same thing.

The advantage of one notation or another comes when you try to do things with it. For example, adding two sinusoidal signals,
$A\sin{(\omega{t}+\theta_A)}+B\sin{(\omega{t}+\theta_B)}=C\sin{(\omega{t}+\theta_C)}$

Using complex, it is very easy to solve for $C$ and $\theta_C$. How would you do that with sin notation?

Thank you so much!
That makes totally sense.

In complex notation Iam able to calculate Phase and Magnitude when looking at the complex plan. In The real notation it is much more difficult.

/Mike