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Apply De Moivre's theorem to write (√3+i) ^5 in the form a+ib , with a, b belongs to R ?
Obtain the polar and exponential representations of z_1 , z_2 and z_1 z_2 , where z_1. = 1/2 - ( 2i) and z_2 = 3+i ?
Q. simplify ∫_1^2▒√(1+1/t^2 +〖(lnt)〗^2+2lnt+1)dt
Evaluate the following integrals
1. ∫
2 + 2z + 2
where C is the circle |z| = 2.
2. ∫
Ln(1−z)dz, where C is the parallelogram with vertices ±i, ±(1+i).
3. ∫ 2π
1 + 3 cos θ
4. ∫
4 − 1
dz. where C is the circle |z + 1| = 1
5. ∫
π − i
dz. where C is the unit circle
verify Cauchy Goursat formula where f(z) = z+1 and D is the region bounded by the triangle with vertices at 0,3 and 3+2i.
An entire function f such that f(x+iy) = u(x)+iv(y) must be of the form f(z)= Az+B with A is a real number and B is a complex number.Is it true?
If f is a complex valued continuous function on C,then I = Integral (f(z)-f(1/z))/z =0 where path if integration is unit circle.Is this statement true?
Sketch the families of curves of component functions u and been f(z)= z-1/z+1