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Complex Analysis Answers

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Given f(z) = x²+y²-2x+4+i(2xy-2y)
Express both f(z) and f'(z) in terms of the complex variable z=x+iy
Find the sum of fifth roots of unity?
Apply De Moivre’s theorem to write (√3+i)^5 in the form a + ib , with
a, b∈ R
Obtain the polar and exponential representations of z1, z2, and z1z2 where z1=1/2 - 2i, and z2=3+i
Express
z=1/(-5-i) in standard (algebraic) form. Further, give an Argand diagram
in which z, z bar and −z are plotted.
Apply De Moivre's theorem to write (√3+i) ^5 in the form a+ib , with a, b belongs to R ?
Obtain the polar and exponential representations of z_1 , z_2 and z_1 z_2 , where z_1. = 1/2 - ( 2i) and z_2 = 3+i ?
Q. simplify ∫_1^2▒√(1+1/t^2 +〖(lnt)〗^2+2lnt+1)dt
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