Complex Analysis Answers

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

verify Cauchy Goursat formula where f(z) = z+1 and D is the region bounded by the triangle with vertices at 0,3 and 3+2i.

What is the argument of z=-4

Show that integral dz/(z^2-1)^2+3=π/2√2, where path of integration is unit circle in the positive sense

Find the image of the half plane y>1 under the transformation w=(1-i)z

Find the value of a belongs to real numbers for which ai is a solution of z^4-2z^3+7z^2-4z+10=0 also find all the roots of this equation

Find all the 8th roots of i3 − 3. Also show any one of them in an Argand diagram.