Question

Determine the roots of the equations:

a) Z^{3} = -4-3i

b) Z^{5} = 1+6i

Answer #1

Find a polynomial in R[x] of minimum degree which has roots 3,
i+1 and -3i.

Consider the following.
Fourth roots of −4
(a) Use the formula
zk =
n
r
cos
θ +
2πk
n
+ i sin
θ +
2πk
n
to find the indicated roots of the complex number. (Enter your
answers in trigonometric form. Let 0 ≤ θ <
2π.)
z0
=
z1
=
z2
=
z3
=
(b) Write each of the roots in standard form.
z0
=
z1
=
z2
=
z3
=

Consider the vectors |a>= (2i, 1-i, 4i) and |b>=(1-3i, 3i,
1-5i) Where I is the imaginary number
a) Normalize each vector |a> and |b>
b) Determine whether these two vectors are orthogonal or not

Determine whether or not x^2+x+1 is irreducible or not over the
following fields. If the polynomial is reducible, factor it.
a. Z2
b. Z3
c. Z5
d. Z7

Let f(x y z)=x4y4+z5,
P=(4, 4, 1).
Calculate the directional derivative in the direction pointing
to the origin. Remember to normalize the direction vector.
(Use symbolic notation and fractions where needed.)
Duf(4, 4, 1)

Let f(x y z)=x4y4+z5,
P=(4, 4, 1).
Calculate the directional derivative in the direction pointing
to the origin. Remember to normalize the direction vector.
(Use symbolic notation and fractions where needed.)
Duf(4, 4, 1)

If we have a competitive industrial form that has the production
function q=z1^(1/4)*z2^(a)z3^(1/4)
q is the output, z1 z2 z3 is the production inputs and a is
parameter.
Assume that production input 2 (z2) is fixed in the short
run
1) Find the short run conditional input demand functions for the
firm
2) Find the short run cost function for the firm
3) Find the short run supply function for the firm
4) what happens to the conditional input demand,...

4. A study was made at the Experimental Station in to determine
the relationship between roots and fungi during which minerals are
transferred from fungi to roots and sugars are transferred from
roots to fungi. Twenty mahogany seeds were taken with the fungus
Pisolithus tinctorus and grown in a nursery. All the seeds were
planted in the same type of soil and received the same amount of
water and sun. Half of them received nitrogen (370 ppm) and the
other...

Determine the center and radius of the following equations and
draw their graph.
(?−0.5)^2−4=(?+1)^2

WRITE MATLAB CODE TO SOLVE THIS!! YOU NEED TO
DETERMINE TWO POSITIVE ROOTS
Determine the two positive roots of f(x) = 7
sin(x)e-x - 1 :
a)Graphically.
b)Using the Newton-Raphson method.
c)Using the secant method.
Initial guesses of x can be decided from the plot and use
maximum iterations. Explain your results.

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