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Complex Analysis
(a) Let z1 = 1 + √2i and 1 −√2i.
(i) Determine the polar form of z1.
(ii) Determine that the polar form of z2.
(iii) Use the polar forms of z1 and z2 to verify that z1 · z2 = 3
(iv) Use the polar forms of z1 and z2 to verify that −1/3 +2/3√2i =z1/z2
(i) Determine the polar form of z1.
(ii) Determine that the polar form of z2.
(iii) Use the polar forms of z1 and z2 to verify that z1 · z2 = 3
(iv) Use the polar forms of z1 and z2 to verify that −1/3 +2/3√2i =z1/z2
Complex Analysis
Complex valued function
Solve w=z1+z2 and find u and v?
Solve w=z1+z2 and find u and v?
Complex Analysis
Solve coshz=2 and separate real and Imaginary part?
Complex Analysis
prove that image of
the vertical line x=k with k is not =0 to the circle mode of w-1/2k = mode of 1/2k
the vertical line x=k with k is not =0 to the circle mode of w-1/2k = mode of 1/2k
Complex Analysis
Find residue
1)- 4/1+z^2
2)- 1/1-e^z
3)- sin2z/z^6
1)- 4/1+z^2
2)- 1/1-e^z
3)- sin2z/z^6
Complex Analysis
Using complex numbers, prove that the, angles A, B and C of a planar triangle satisfy the relations
(i) cos^2 A + cos^2 B + cos^2 C = 1 − 2 cos A cos B cos C
(ii) sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C.
Complex Analysis
Express cos^4
θ sin^3
θ in terms of multiples of angles.
θ sin^3
θ in terms of multiples of angles.
Complex Analysis
For the function
f(z)=1/(z²(1 + z + 2z2))
,
find the first three terms of the Laurent Series expansion of f about a = 0 that converges
in the deleted disk D'(0, δ) for some δ > 0
f(z)=1/(z²(1 + z + 2z2))
,
find the first three terms of the Laurent Series expansion of f about a = 0 that converges
in the deleted disk D'(0, δ) for some δ > 0
Complex Analysis
The equation z-3i-3=z+i+2 in z=x+iy with x,y belongs to R describes the line
Complex Analysis
Prove that for Re(s) >1,we have phi(s) =s integral from 1 to infinity f(x)/x^{s+1} dx
