Given z = 5 - 2i. Determine the following: a) Re(z) b) Im(z) c)
Arg(z) d)...
Given z = 5 - 2i. Determine the following: a) Re(z) b) Im(z) c)
Arg(z) d) arg(z) e) conjugate(z) f) modulus(z) g) z in polar form
h) z in exponential form i) z^2 in polar form.
Draw a sketch of z ∈ C | Im((3 − 2i)z) > 6 .
2. Express z = −i − √ 3 in the form r cis θ where θ = Argz.
3. Use de Moivre’s theorem to find the two square roots of
−4i.
Define the following order on the set Z × Z: (a, b) < (c, d)
if either a < c or a = c and b < d. This is referred to as
the dictionary order on Z × Z.
(a) Show that there are infinitely many elements (x, y) in Z × Z
satisfying the inequalities (0, 0) < (x, y) < (1, 1).
(b) Show that Axioms O1–O3 ( Trichotomy, Transitivity, Addition
for inequalities) are satisfied for this...
Let R be the relation on Z+× Z+ such that (a, b) R (c, d) if and
only if ad=bc. (a) Show that R is an equivalence relation. (b) What
is the equivalence class of (1,2)? List out at least five elements
of the equivalence class. (c) Give an interpretation of the
equivalence classes for R. [Here, an interpretation is a
description of the equivalence classes that is more meaningful than
a mere repetition of the definition of R. Hint:...
The following scores are given in Periods of A, B, C, and D of a
high school. Test the claim that there is a significant difference
among the 4 mean scores of these 4 periods. Use a significance
level of .05.
A
B
C
D
10
11
13
18
9
16
8
23
5
9
9
25
Step 1: Claim: Ho: Ha:
Step 2: Significance level:
Step 3: Test
Values for each required entry on calculator:
P-value:
Step 4: Decision...
Define a relation ~ on Z x Z such that (a,b) ~ (c,d) precisely
when a + b = c + d.
Let R = {[(a,b)] : (a,b) in Z x Z} (i.e. R is the set of all
equivalence classes of Z x Z under the equivalence relation ~). For
each of the following operations, determine whether or not the
operation is well defined. Prove your answer.
[(x,y)] * [(w, z)] = [(x + w, y + z)]
[(x,y)]...
In the following sentences determine the appropriate sampling A,
B, C or D
A --- RANDOM (SIMPLE RANDOM SAMPLING)
B --- SYSTEMATIC
C --- STRATIFIED
D --- Cumulative (CONGLOMERATES)
1- A company is divided by DIRECTIVES, EMPLOYEES, SECRETARIES
AND WORKERS. It is wanted to make a study to know the level of
satisfaction in relation to the benefits that the company has. The
head of human resources decides to take a random sample of each
category.
2- A university career...
Analyze following logic expression representing a
digital system,
Z = (A+C)(A'+D')(B'+C'+D)
Identify the 0-hazards and write down the logic expression for the
implementation of static free
circuit. Note that you would be requiring three additional loops in
K-map.
What is meant by chemical equilibrium? Given the
following reaction: A + B <--> C +D (reversible
reaction), how would you drive the following reaction away
from equilibrium to produce more of substances A and
B?