plz i need full solution on this i haven't been taught b4...i was give this to solve plz plz help me

Question

integral(dz/(|z|)²)

Answer 1

| z |² = z²

∫ dz / | z |² = ∫ dz / z² = ∫ z ⁻² dz
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Apply the power rule​:

∫ xⁿ dx = xⁿ⁺¹ / ( n + 1 ) + C
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∫ z⁻² dz = z ⁻²⁺¹ / ( - 2 + 1 ) + C = z ⁻¹ / ( - 1 ) + C = - z ⁻¹ + C = - 1 / z + C

∫ dz / | z |² = - 1 / z + C

Answer 2

the question say i should use green's theorem

Answer 3

Are we dealing with a complex variable z, so that Green's Theorem states that
∫B(z,z*) dz = 2i ∫∫∂B/∂z* dx dy
So, we have B(z,z*) = zz*
and |z|^2 = x^2+y^2
?? Or are we just dealing with a vector function z = xi+yj+zk ??

Answer 4

yes complex variable z..pls ,show me how pls pls

yes yes