(d) Let x be the complex number 1-i. Use de Moivre's Theorem to find the smallest n E N such that x" is a real number. 4 / 4
(d) Let x be the complex number 1-i. Use de Moivre's Theorem to find the smallest n E N such that x" is a real number. 4 / 4
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...
Related questions
Question
Part d please
![Question 5
(a) Suppose R is a relation on a set X. Define what it means to say that R is transitive.
(b) Decide whether each of the following relations is transitive. [No justification is required - just
write "yes" or "no" for each case.]
(i) The relation R on Z defined by aRb if a b + 1.
(ii) The relation R on Z defined by aRb if a² = b².
(iii) The relation R on Z x Z defined by (a, b)R(c, d) if ad = bc.
(c) Let z be the complex number 4 - 3i. Find the following. [You do not need to show your
working, but doing so may help you to gain marks if you make arithmetic errors.]
(iv) z².
(v) A complex number w such that wz = Z.
(d) Let x be the complex number 1 - i. Use de Moivre's Theorem to find the smallest n E N
such that x" is a real number.
<
4
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b36c913-0209-42a1-b7f1-f4674ddc09d4%2F9a33ef21-cf11-44a2-9438-9a7fe2c86609%2Flyuk66m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 5
(a) Suppose R is a relation on a set X. Define what it means to say that R is transitive.
(b) Decide whether each of the following relations is transitive. [No justification is required - just
write "yes" or "no" for each case.]
(i) The relation R on Z defined by aRb if a b + 1.
(ii) The relation R on Z defined by aRb if a² = b².
(iii) The relation R on Z x Z defined by (a, b)R(c, d) if ad = bc.
(c) Let z be the complex number 4 - 3i. Find the following. [You do not need to show your
working, but doing so may help you to gain marks if you make arithmetic errors.]
(iv) z².
(v) A complex number w such that wz = Z.
(d) Let x be the complex number 1 - i. Use de Moivre's Theorem to find the smallest n E N
such that x" is a real number.
<
4
4
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning