Consider a complex function

F(s)=(1)/(s+1)

of a complex variable

s

.\ (a) Assume

s=-\\\\sigma +j\\\\omega

where

\\\\sigma

and

\\\\omega

are real numbers. Obtain the magnitude and phase of

F(s)

in terms of

\\\\sigma

and

\\\\omega

.\ (b) Now set

\\\\sigma =0

, so that

s=j\\\\omega

. Obtain real and imaginary parts of

F(s)

in terms

\\\\omega

.\ (c) We want to see how

F(s)

varies as

s=j\\\\omega

varies between

-100j

and

100j

(that is when

\\\\omega

increases from -100 to 100.) Write a short MATLAB program to plot the variations of complex function

F(s)

in the complex plane (Hint: Plot the imaginary part of

F(s)

versus its real part as

s

varies from

-100j

to

100j

.)

3. Consider a complex function F(s)=s+11 of a complex variable s. (a) Assume s=+j where and are real numbers. Obtain the magnitude and phase of F(s) in terms of and . (b) Now set =0, so that s=j. Obtain real and imaginary parts of F(s) in terms . (c) We want to see how F(s) varies as s=j varies between 100j and 100j (that is when increases from -100 to 100.) Write a short MATLAB program to plot the variations of complex function F(s) in the complex plane (Hint: Plot the imaginary part of F(s) versus its real part as s varies from 100j to 100j.)