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Find the sum of the 5th roots of unity.
Apply De Moivre’s theorem to write (√3+i)^5 in the form a + ib , with
a, b∈ R
a, b∈ R
Obtain the polar and exponential representations of z1, z2, and z1z2 where z1=1/2 - 2i, and z2=3+i
Express
z=1/(-5-i) in standard (algebraic) form. Further, give an Argand diagram
in which z, z bar and −z are plotted.
z=1/(-5-i) in standard (algebraic) form. Further, give an Argand diagram
in which z, z bar and −z are plotted.
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. ∫
C
z
2
z
2 + 2z + 2
where C is the circle |z| = 2.
2. ∫
C
Ln(1−z)dz, where C is the parallelogram with vertices ±i, ±(1+i).
3. ∫ 2π
0
1
1 + 3 cos θ
dθ.
4. ∫
C
z
2
z
4 − 1
dz. where C is the circle |z + 1| = 1
5. ∫
C
e
z
π − i
dz. where C is the unit circle
1. ∫
C
z
2
z
2 + 2z + 2
where C is the circle |z| = 2.
2. ∫
C
Ln(1−z)dz, where C is the parallelogram with vertices ±i, ±(1+i).
3. ∫ 2π
0
1
1 + 3 cos θ
dθ.
4. ∫
C
z
2
z
4 − 1
dz. where C is the circle |z + 1| = 1
5. ∫
C
e
z
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.
What is the argument of z=-4
