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## Homework Statement

Consider the set V + {all periodic *complex* functions of time t with period 1} Draw two example functions that belong to V.

Show that if f(t) and g(t) are members of V then so is f(t) + g(t)

## Homework Equations

## The Attempt at a Solution

f(t) = e

^{(i*w0*t)})

g(t) =e

^{(i*w0*t +φ)})

Where W

_{0}= 2*π

Using 'Euler's' I can write these as;

f(t) =cos(w

_{0}*t) + i*sin(w

_{0}*t)

g(t) =cos(w

_{0}*t +φ) + i*sin(w

_{0}*t +φ)

So for part a) I would plot these functions separating the real and imaginary parts and choosing a value for φ to illustrate the phase shift?

Partb) f(t) + g(t) = e

^{(i*w0*t)}) + e

^{(i*w0*t +φ)})

= (1 + e

^{φ}) * e

^{i*w0*t}

The signal remains a periodic complex function of t with a period of 1 and is therefore a member of V.

Thanks

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