- #1

- 17

- 0

e^+-(ix) = cos(x) +- isin(x)

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1. A complex number can be written in rectangular coordinates as z = x+ jy. Write the relations to calculate the

polar form, z = (r,theta) or z = re^(j*theta) .

For this one im more confused about what he's asking or how to show the work... i think

r = sqrt(x^2 + y^2)

and

theta = tan^-1(y/x)

But i'm not really sure if thats what he's looking for

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3. Convert cos(wt + f) into the sum of complex exponentials.

Now i know that cos(x) = (e^(ix) + e^-(ix))/2

Is this as simple as replacing x with (wt + f)?

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5. Compute [(1+ i*sqrt(3))/2]^2 and (1 + j)^4

a) directly (using rectangular representation)

b) using complex exponentials

How do i go about this for both of these approaches, im not entirely sure how to do either approach.