MTH305
Question: Express \\(-3i\\) in polar form
Answer: \\(3e^(3Ï€i/2)\\)
Question: Find the derivative of \\( f(z)=z^3-2z\\) at the point where \\(z=1\\)
Answer: 1
Question: Find all points of discontinuity for the complex function \\(f(z)=\\frac{(2z-3)}{(z^2+2z+2)}\\).
Answer: \\(-1 ± i\\)
Question: If \\(A(x,y)=2xy-ix^2 y^3\\), find \\(div A\\).
Answer: \\(2y-3x^2 y^2\\)
Question: Evaluate \\(lim_{z\\longrightarrow 2i}\\frac{(2z+3)(z-1)}{z^2-2z+4}\\)
Answer: \\(-1/2+11/4 i\\)
Question: Find an analytic function \\(f(z)\\) such that \\( Re{f^\’ (z)}=3x^2-4y-3y^2 and \\(f(1+i)=0\\).
Answer: \\(z^3+2iz^2+6-2i\\)
Question: Given that the series\\( 1 + i /3 + (i/3)^2 +⋯ =∑ _{n=1}^∞(i/3)^{n -1}\\) converges. Find its sum.
Answer: \\( (9+3i)/10\\)
Question: If \\(z_1=1-i\\) and \\(z_2=-2+4i\\) , evaluate \\( |z_1 \\overline{z_2}+ z_2 \\overline{z_1}\\)|
Answer: 12
Question: Evaluate \\(lim_{z\\longrightarrow ∞) \\frac{z^3-3z+2}{z^4+z^2-3z+5}\\)
Answer: \\(0\\)
Question: Evaluate\\( (5+5i)/(3-4i)+20/(4+3i) \\)
Answer: 3-i
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