Find the amplitude fundamental period frequency and phase

Question

Question 1.  Express each of the following complex numbers in Cartesian form ( x + jy):

a. (1/2)e^jπ

b. √2 e^(-jπ/4)

Question 2. Express each of the following complex numbers in polar form (re^θ, with -π< θ ≤π):

a. 1 + j

b. j (1-j)

c. (1 + j ) / (1 - j)

d. -3 j

Question 3. Find the Amplitude, fundamental period, frequency and phase for the following sine wave

a. s₁(t)=10sin?(2000πt+(π/3 ))

b. s₂(t)=sin?(5πt-π)

Question 4. Plot the following signals

a. sin?(2πt),

b. sin?(2πt+(π/2 ))

c. sin?(2πt+π)

d. sin?(2πt+(3π/2 ))

Question 5. Plot the frequency component of signal

4 sin?(200πt+(π/3 ))+sin?(10πt-π)

What is the bandwidth of this signal?