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Declare complex numbers e.g.  z1=3+4i,  z2=4-7i. Discuss their algebra  z1+z2,  z1-z2,  z1*z2 and z1/z2 and plot them. Also, do the same for  z1=6-5i  and  z2=3+7i.

Find conjugate, modulus and phase angle of an array of complex numbers, e.g. Z={2+3i, 4-2i, 6+11i, 2-5i} and plot them for a complex number.

Compute the integral of a complex function over a straight line path between the two specified end points as a+ib and c+id.

Perform contour integration for complex function with contour C, which is given by g(x,y)=0.

Plot the complex function, e.g.  f(z)=z^3  and  f(z)=(z^2+1)^2.

Find the residue of complex functions. e.g.  f(z)=1/z,  f(z)=sin(z)/z^2,  f(z)=z^3  etc.

Taylor series expansion of a given function f(z) around a given point z, given the number of terms in the Taylor series expansion. Hence comparing the function and it's Taylor series expansion by plotting the magnitude of each.

Laurent series expansion of a given complex function f(z) around a given point z. 

(i)  f(z)=(Sin(z)-1)/z^4  around z=0,  (ii)  f(z)=Cot(z)/z^4  around z=0.

Compute Fourier series, Fourier sine series and Fourier cosine series of a complex function and plot their graphs, such as f(z)= z^2  and  f(z)=sin(z).

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