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Complex Analysis Answers

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simplify this complex number
cos3x + jsin3x / cosx + jsinx
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
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 ?
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