Question

Find all the complex number z such that z^2=i

Answer #1

12.

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(1) Find all functions f(z) that are analytic in the entire
complex plane and satisfy 2|sin(z)| ≥ |f(z)|.
(2) Find all functions f(z) that are analytic in the entire
complex plane and satisfy 2|f(z)| ≥ |sin(z)|.

. In this question, i ? C is the imaginary unit, that is, the
complex number satisfying i^2 = ?1. (a) Verify that 2 ? 3i is a
root of the polynomial f(z) = z^4 ? 7z^3 + 27z^2 ? 47z + 26 Find
all the other roots of this polynomial. (b) State Euler’s formula
for e^i? where ? is a real number. (c) Use Euler’s formula to prove
the identity cos(2?) = cos^2 ? ? sin^2 ? (d) Find...

Complex analysis
For the function f(z)=1/[z^2(3-z)], find all possible Laurent
expansions centered at z=0.
then find one or more Laurent expansions centered at z=1.

Complex Variables:
(a) Describe all complex numbers 'z' such that e^z = 1.
(b) Let 'w' be a complex number. Let 'a' be a complex number
such that e^a = w. Describe all complex numbers 'z' such that e^z =
w.

Complex Analysis
2. Find the linear transformation which carries the circle |z| =
2 into |z + 1| = 1, the point −2i into the origin, and the point i
into −1.

Using the same complex number p=4+6i, create 'a new personal
complex number z= x+ iy = p e^(i theta) where theta 10. .Then
)calculate a) What are r = |z| and θ = arg(z)? (b)Find the two
values of √ z in polar form. As in (a), please state which
quadrants your answers are in. (c) Find all values of ln(z). How
many are there. Also in part (a), identify which 45-degree "pizza
slice" your angle is in, if you...

If z is a complex number. Find the Taylor's series expansion of
Log(1+z) about 0 and find the radius of convergence. Show each
detail step

Convert the following complex number to polar form,
z= -(sqrt(3))/3+(i/3)

If z=4e^(i pi/4) and w=3e^(i pi/3) find
a) zw
b) z/w
c) z^3
d) The complex fourth root of w

Complex Variable
Evaluate the following:
A) ∫_∣z−i∣=2 (2z+6)/(z^2+4) dz
B) ∫_∣z∣=2
1/((z−1)^2(z−3)) dz ( details
please)
C) ∫_∣z∣=1 e^(4/z) dz

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