Complex Analysis Answers

find the inverse laplace transform of F (S)=10 (S+1)/S (S+2)(S+3)^3

Prove or disapprove that the complex sphere is compact.

The locus of the complex number arg(z^* + i√3) - π/4 is equal to?

Find the general solution of the differential equation dy/dx = xy / (x+2)(x+1) expressing y explicitly in terms of x.

Find the general solution of each differential equation, expressing y explicitly in terms of x.

5) dy/dx = x(y+1)

Given that the complex number z and its conjugate z* satisfy the equation zz* + 2iz = 12 +6i. Find the possible value of z.

The two complex numbers z₁ and z₂ are represented on an argand diagram. Show that

Iz₁ + z₂I ≤ Iz₁I +Iz₂I. If Iz₁I = 6 and Iz₁I = 4+3i, Show that the greatest value of Iz₁ + z₂I is 11 and find its least value.

Using the fact that if z = r(cosθ +isinθ) then z² = r²(cosθ +isinθ), find the square root of

2√3 -2i

The locus of the complex number arg(z^* + i√3) - π/4 is equal to?