# imaginary and real world signals

#### bhuvanesh

Joined Aug 10, 2013
268
my professor signals and system talk"we have two signals real signal and imaginary signals.WE CAN PLAY WITH IMAGINARY SIGNALS but cannot with real signals and we can always transform imaginary signals into real signals"

could anyone understand what he trying to say.Why does he say we can play with imaginary signals

#### WBahn

Joined Mar 31, 2012
25,096
I would need a better idea of the context within which the statement is made, but my guess is that all he is saying is that we can transform a real world signal representation into a representation that involves complex numbers and then work (i.e., "play") with that representation and then, at the end of the day, transform the final result back into a real world signal representation.

This is exactly what we do when we convert an sinusoidal signals into "phasors", transform inductances and capacitances into "impedances", or take the Laplace or Fourier transform of signals.

#### bhuvanesh

Joined Aug 10, 2013
268
how do you convert real signal into imaginary signal.example i have cos and sine signal. Now how do you convert it to imaginary signal

#### WBahn

Joined Mar 31, 2012
25,096
We were leading up to that in the thread on complex exponentials, but you bailed on it.

#### bhuvanesh

Joined Aug 10, 2013
268
sorry sir,actually i was in hurry to reply so didnt think of past,Thanks

#### bhuvanesh

Joined Aug 10, 2013
268
i am sailing in boat moving 3 units in north moving 4 units in east having 3+4j as vector now i want to rotate it to 90 degree counter clockwise so i just multiply by i.Then i get the answer ,but i want to know it can be done in harder way,i mean how to do same rotation with using complex plane .THank you in advance

#### WBahn

Joined Mar 31, 2012
25,096
What do you mean by "how to do the same rotation with using complex plane"? You just did it using the complex plane.

Try doing it with trig and unit vectors, instead.

By convention, "north" is the +y axis (the imaginary axis) and "east" is the +x axis (the real axis).

$$V_1 \; = \; 4m \hat x + 3m \hat y \; = \; 5m \angle 36.87^\circ$$

So find V2 which is V1 rotated 90^\circ counterclockwise

$$V_2 \; = \; 5m \angle \( 36.87^\circ+90^\circ$$
\)

And crank the trig handle to get that into rectangular coordinates.

#### bhuvanesh

Joined Aug 10, 2013
268
corrected:how to do same rotation without using complex plane
ya that is by using trig
A stranger in comment gave this
x’= xcosa -ysina
y’= xsina +ycosa
x' and y' are new co-ordinates and x and y are old co-ordinates and a is angle
where does this formula come from

#### WBahn

Joined Mar 31, 2012
25,096
corrected:how to do same rotation without using complex plane
ya that is by using trig
A stranger in comment gave this
x’= xcosa -ysina
y’= xsina +ycosa
x' and y' are new co-ordinates and x and y are old co-ordinates and a is angle
where does this formula come from
From basic trig and the application of basic trig identities.

I know you are trying very, very hard to grasp this stuff, but you mostly appear to be flailing around from topic to topic without developing the basic, foundation math knowledge and skills upon which all of this stuff is built. You can't hope to pick this stuff up piecemeal. It would be like someone trying to learn how to compose a symphony but constantly having to ask if D-flat is the same as C-sharp and not knowing that the interval between some adjacent notes is a full tone while others are a semi-tone. Your only hope is to go back and learn the foundational material. From what I have seen, that means at least going back to introductory algebra and learning it and mastering it. Then geometry. Then trigonometry. Then calculus. Along the way you need to pick up exponentials, logarithms, and complex numbers.