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Complex Analysis

Q: Evaluate the following integral using residue theorem

∫ Z^2 e^z dz ; C : |z| = 1 ,Answer(πi/3)

∫ Z^2 e^z dz ; C : |z| = 1 ,Answer(πi/3)

Complex Analysis

Q: Evaluate the following integral using residue theorem

∫ coth z / (z-i) dz ; C : |z| = 2

∫ coth z / (z-i) dz ; C : |z| = 2

Complex Analysis

show that the function f(z)=1/a+z/a^2+.....can be continued analytically

Complex Analysis

evaluate close integrals :

closed integral at c 1/(z^4+1) dz with contour c:|z|=4

closed integral c 1/(z^4+10z+9) dz with c:|z|=2

closed integral c e^z/(z^4+5z^3) dz with c:|z|=2

closed integral at c 1/(z^4+1) dz with contour c:|z|=4

closed integral c 1/(z^4+10z+9) dz with c:|z|=2

closed integral c e^z/(z^4+5z^3) dz with c:|z|=2

Complex Analysis

Let w be a complex number, z a 4th root of w.

1) Show that z(k) = p^1/4[cos((θ + 2kπ)/4) + isin((θ + 12kπ)/4)], k = 0, 1, 2, 3, is a formula for the 4th roots of w, where θ is the argument of w and p its modulus.

2) hence , determine 4th roots of 16.

please assist.

1) Show that z(k) = p^1/4[cos((θ + 2kπ)/4) + isin((θ + 12kπ)/4)], k = 0, 1, 2, 3, is a formula for the 4th roots of w, where θ is the argument of w and p its modulus.

2) hence , determine 4th roots of 16.

please assist.

Complex Analysis

Using De Moivre's theorem or otherwise

find the six roots of the equation z^6 +1 = 0

giving your answers in the form e^iw where w= angle teta

find the six roots of the equation z^6 +1 = 0

giving your answers in the form e^iw where w= angle teta

Complex Analysis

Find the original function without finding the corresponding conjugate

u(x,y)=e^xcosy

u(x,y)=e^xcosy

Complex Analysis

Find the original function without finding the corresponding conjugate

u(x,y)=x/x^2+y^2

u(x,y)=x/x^2+y^2

Complex Analysis

Prove that u(x,y) given by the following is harmonic obtain it's corresponding conjugate and original function f(z)

u(x,y)=e^xCosy

u(x,y)=e^xCosy

Complex Analysis

Prove that u(x,y) given by the following is harmonic obtain it's corresponding conjugate and original function f(z)

u(x,y)=x^2-y^2

u(x,y)=x^2-y^2