# Thread: [SOLVED] complex numbers amplitude and phase - complex amplitude?

1. ## [SOLVED] complex numbers amplitude and phase - complex amplitude?

I have a problem

find the amplitude and plot the phase of the complex number

$\displaystyle j e^{(1+j)\pi t}$

I have an exam tomorrow and this may come up not sure where to start, its basically the j at the start that is throwing me off, as i did not think it was possible to have a complex amplitude since it should be square root of the modulus.

2. Originally Posted by checkthiskid
I have a problem

find the amplitude and plot the phase of the complex number

$\displaystyle je^{(1+j)\pi t}$

I have an exam tomorrow and this may come up not sure where to start, its basically the j at the start that is throwing me off, as i did not think it was possible to have a complex amplitude since it should be square root of the modulus.

Note that $\displaystyle j = e^{j \pi/2}$.

3. thanks seems kinda obvious when you say that

4. actually iv ended up with

$\displaystyle e^{j(\pi/2 + \pi t)+ \pi t}$

that means part of the phase is not a multiple of j that cant be right?

(sorry dnt know how to use that equation tool)

or does that mean that the amplitude varies with t? with an amplitude of $\displaystyle e^{\pi t}$

5. Originally Posted by checkthiskid
actually iv ended up with

$\displaystyle e^{j(\pi/2 + \pi t)+ \pi t}$

that means part of the phase is not a multiple of j that cant be right?

(sorry dnt know how to use that equation tool)

or does that mean that the amplitude varies with t? with an amplitude of $\displaystyle e^{\pi t}$
$\displaystyle e^{j(\pi/2 + \pi t)+ \pi t} = e^{\pi t} \cdot e^{j (\pi/2 + \pi t)}$.

The amplitude is $\displaystyle e^{\pi t}$ and the phase (argument) is $\displaystyle \frac{\pi}{2} + \pi t$.

6. Shouldn't the argument be $\displaystyle \frac{\pi}{2}+\pi t$?

7. Originally Posted by chiph588@
Shouldn't the argument be $\displaystyle \frac{\pi}{2}+\pi t$?
yeah got it now thanks