Topic: Review of Complex Numbers

## Question

Compute the Magnitude of the following continuous-time signals a) $x(t)=e^{2t}$

b) $x(t)=e^{2jt}$

What properties of the complex magnitude can you use to check your answer?

a) $|e^{(2t)}| = \sqrt{(e^{(2t)})^2} = \sqrt{e^{(4t)}} = e^{(2t)}$ (cmcmican 10:59, 10 January 2011 (UTC))

b) $|e^{(2jt)}| = |(cos(2t) + j*sin(2t))| = \sqrt{(cos(2t))^2 + (sin(2t))^2} = \sqrt{1} = 1$ (cmcmican 10:59, 10 January 2011 (UTC))

Instructor's comments: Both answers and justifications are correct. Note that an alternative method to obtain the complex magnitude of the signal in b) is to multiply the signal value by its complex conjugate and taking the square root of the result. (This is basically what you are doing in a), but since the signal is real, it is equal to its conjugate.) A quick note though on the symbol $*$: we will be using it to denote the convolution operation later on, so it will be important not to use it to denote multiplication anymore. -pm 