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Complex Analysis Answers

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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
Choose the correct answer.
Q. The residue of f(z)=sinh⁡z/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)=sin⁡z/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
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
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
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