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Q. Which of the following is image of straight line x=1 under the transformation f(z)= z^2, where z=x+iy?

a. A circe

b. An ellipse

c. A parabola

d. A hyperbola

Q. Which of the following is image of straight line x=1 under the transformation f(z)= z^2, where z=x+iy?

a. A circe

b. An ellipse

c. A parabola

d. A hyperbola

Choose the correct answer.

Q. The residue of f(z)=sinhz/z^6 is

a. 1/6!

b. 1/4!

c. 0

d. 1

Q. The residue of f(z)=sinhz/z^6 is

a. 1/6!

b. 1/4!

c. 0

d. 1

Q.Choose the correct answer.

Q. Which of the following statement is true for f(z)=sinz/z^4 ?

a. f has essential singularity at z=0.

b. f has pole of order 3 at z=0

c. f has removable singularity at z=0.

d. None of above

Q. Which of the following statement is true for f(z)=sinz/z^4 ?

a. f has essential singularity at z=0.

b. f has pole of order 3 at z=0

c. f has removable singularity at z=0.

d. None of above

Q.Choose the correct answer.

Q. Let C=|z-2|=5, then evaluate the complex integral ∫_C▒〖(z^4 〗+4z)〖cos〗^2 zdz

a. 1

b. 0

c. π

d. -1

Q. Let C=|z-2|=5, then evaluate the complex integral ∫_C▒〖(z^4 〗+4z)〖cos〗^2 zdz

a. 1

b. 0

c. π

d. -1

Find the polynomial equation over R of lowest degree which is satisfied by 1-i and 3+2i

Find the polynomial equation over R of lowest degree which is satisfied by 1-i and 3+2i

Describe the geometric, polar and exponential representations of:

(\bar -5i+2)⁻¹

(\bar -5i+2)⁻¹

If ω is a cube root of unity show that (1-ω+ω²)(1+ω-ω²)=4

What is the distance between the points x and y, given that x = 3 + 2i and y = 4 + 3i?

Question: please convert this complex number into the polar form.

1/2j

note: it is not (1/2) * j

it is 1/2*j --> j is at denominator

1/2j

note: it is not (1/2) * j

it is 1/2*j --> j is at denominator