Questions and answers: Complex Analysis 1

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69 Questions  View: All | Solved | Unsolved

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• Let w = 3z + 4 – 5i = f(z) Find the values of w which corresponds to z = -3 + i on the z...(Solved)
  

  Let w = 3z + 4 – 5i = f(z) Find the values of w which corresponds to z = -3 + i on the z plane.

  Date posted: May 10, 2019.  

• Find the image of the point (4, 3) on z plane under the transformation w = 2z² + 3.(Solved)
  

  Find the image of the point (4, 3) on z plane under the transformation w = 2z² + 3.

  Date posted: May 10, 2019.  

• Prove that sin z = sin x cos hy + i cos x sin hy(Solved)
  

  Prove that sin z = sin x cos hy + i cos x sin hy

  Date posted: May 10, 2019.  

• Find all values of z such that(Solved)
  

  Find all values of z such that

  Date posted: May 10, 2019.  

• Find all values of z such that e^z = 2(Solved)
  

  Find all values of z such that e^z = 2

  Date posted: May 10, 2019.  

• Show that(Solved)
  

  

  Date posted: May 10, 2019.  

• Prove that(Solved)
  

  

  Date posted: May 10, 2019.  

• Show that the function;(Solved)
  

  Show that the function; is not analytic at the origin, although the Cauchy –Reimann equations are satisfied at the origin.

  Date posted: May 10, 2019.  

• Let f (z) = u(x, y) + iv(x, y) .Prove that(Solved)
  

  Let f (z) = u(x, y) + iv(x, y) .Prove that

  Date posted: May 10, 2019.  

• Let f(z) = u +iv be an analytic function. If u = u³ – 3x²y find f(z).(Solved)
  

  Let f(z) = u +iv be an analytic function. If u = u³ – 3x²y find f(z).

  Date posted: May 10, 2019.  

• If the real part of an analytic function f(z) = u + iv is given, then(Solved)
  

  If the real part of an analytic function f(z) = u + iv is given, then prove.

  Date posted: May 10, 2019.  

• Prove the Cauchy – Reimann Equations(Solved)
  

  Prove the Cauchy – Reimann Equations

  Date posted: May 10, 2019.  

• Define an entire function(Solved)
  

  Define an entire function

  Date posted: May 10, 2019.  

• Define analytic function in a Region R.(Solved)
  

  Define analytic function in a Region R.

  Date posted: May 10, 2019.  

• Define analytic function(Solved)
  

  Define analytic function

  Date posted: May 10, 2019.  

• Derive of a function of complex variables.(Solved)
  

  Derive of a function of complex variables.

  Date posted: May 10, 2019.  

• For what values of z is the following function continuous? (Solved)
  

  For what values of z is the following function continuous?

  Date posted: May 10, 2019.  

• Show that the following function is not continuous at z = i(Solved)
  

  Show that the following function is not continuous at z = i

  Date posted: May 10, 2019.  

• Prove that f(z) = 2z² is continuous at z = z₀(Solved)
  

  Prove that f(z) = 2z² is continuous at z = z₀

  Date posted: May 10, 2019.  

• Prove that(Solved)
  

  

  Date posted: May 10, 2019.  

• If a + ib is a root of a polynomial, a₀zⁿ +a₁z^n-1 +...........+a_n =0 a₀, a₁…a_n are real number. show that its conjugate a – ib is also...(Solved)
  

  If a + ib is a root of a polynomial, a₀zⁿ +a₁z^n-1 +...........+a_n =0 a₀, a₁…a_n are real number. show that its conjugate a – ib is also a root of the same equation or the zeros of a polynomial with real coefficients always occur in conjugate pairs.

  Date posted: May 2, 2019.  

• Find all the 6^th roots of unity.(Solved)
  

  Find all the 6^th roots of unity.

  Date posted: May 2, 2019.  

• Find the square roots of –15 – 8i(Solved)
  

  Find the square roots of –15 – 8i

  Date posted: May 2, 2019.  

• Solve the equation z⁴ - 16 = 0(Solved)
  

  Solve the equation z⁴ - 16 = 0

  Date posted: May 2, 2019.  

• Solve the equation z³ = -1³= -1 giving three values of the roots.(Solved)
  

  Solve the equation z³ = -1³= -1 giving three values of the roots.

  Date posted: May 2, 2019.  

• Simplify the expression below;(Solved)
  

  Simplify the expression below;

  Date posted: May 2, 2019.  

• Given z₁ and z₂,show that.(Solved)
  

  Let show that

  Date posted: May 2, 2019.  

• Simplify the expression below;(Solved)
  

  Simplify the expression below;

  Date posted: May 2, 2019.  

• Simplify the expression given below;(Solved)
  

  Simplify the expression given below;

  Date posted: May 2, 2019.  

• Express z = 4 + 3i in polar form(Solved)
  

  Express z = 4 + 3i in polar form

  Date posted: May 2, 2019.