Converting phasor to time domain

[CoolDude420]

Homework Statement

Homework Equations

The Attempt at a Solution

I am extremely confused. Everywhere I go to look on how to convert phasors into time domain I get a different answer. I am trying to convert -j to the time domain. My notes says to find the Im(phasor). I have explained in the image above what my lecture notes say, what the question is and what my answer is.

Here is the provided answer in the notes:

Can anyone provide me with a universal method ?

 

[NascentOxygen]

I am trying to convert -j to the time domain.

First, sketch the given phasor on the complex plane, with x-axis Real and y-axis Imaginary.

 

[CoolDude420]

 

[NascentOxygen]

Right.

There is a standard way to describe angles, on a graph. What angle would you associate with the line you have drawn? (For this angle, we need both magnitude and sign.)

 

[CoolDude420]

Right.

There is a standard way to describe angles, on an graph. What angle would you associate with the line you have drawn? (For this angle, we need magnitude and sign.)

Measuring from the positive side of the X axis, I would say an angle of -90degrees.

 

[CoolDude420]

Angle should be -90 degrees I think. or - pi/2 rads

 

[rude man]

_peakI am extremely confused. Everywhere I go to look on how to convert phasors into time domain I get a different answer. I am trying to convert -j to the time domain. My notes says to find the Im(phasor). I have explained in the image above what my lecture notes say, what the question is and what my answer is.

Here is the provided answer in the notes:

Can anyone provide me with a universal method ?

Note that (1) the frequency (1000 Hz here) is not included in the phasor.
(2) you have assumed 1V peak. More generally, a phasor is V_pkexp(jθ) ⇔ V_pksin(ωt + θ).
But you have the phase right; -j = exp(-jπ/2). This is an identity. And -jπ/2 = -90 deg so the phase is -90 deg and the time expression is what you wrote above.

 

[NascentOxygen]

Angle should be -90 degrees I think. or - pi/2 rads

Right. That's the angle/phase taken care of.

What is the magnitude (i.e., length) of the line you drew on that graph?