Homework Help is Here – Start Your Trial Now!
Math
Calculus
2. The set of complex numbers can be defined as the set C = {a + bi | a, b = R, i²=-1}. For any complex number z = a +bi € C, • the real part of z is Re(z) = a and the imaginary part of z is Im(z) = b; the conjugate of z is z = a - bi; and • the modulus of z is |z| = √a² + b². With this notation, answer the following (each can be done in one line of computation). 2+z z-z (a) Show that Re(z) = 2 2i (b) Show that z-z = |z|². and Im(z) = (c) Show there is an expression for the multiplicative inverse of z, the number in terms of just the conjugate 7 and the modulus |z|. (Hint: Refer to (b).)

2. The set of complex numbers can be defined as the set C = {a + bi | a, b = R, i²=-1}. For any complex number z = a +bi € C, • the real part of z is Re(z) = a and the imaginary part of z is Im(z) = b; the conjugate of z is z = a - bi; and • the modulus of z is |z| = √a² + b². With this notation, answer the following (each can be done in one line of computation). 2+z z-z (a) Show that Re(z) = 2 2i (b) Show that z-z = |z|². and Im(z) = (c) Show there is an expression for the multiplicative inverse of z, the number in terms of just the conjugate 7 and the modulus |z|. (Hint: Refer to (b).)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
2. The set of complex numbers can be defined as the set C = {a + bi | a, b = R, i²=-1}. For any complex number z = a + bi € C, • the real part of z is Re(z) = a and the imaginary part of z is Im(z) = b; the conjugate of z is z = a -bi; and • the modulus of z is |z| = √a² + b². With this notation, answer the following (each can be done in one line of computation). 2+z z-z (a) Show that Re(z) = 2 2i (b) Show that · z = |z|². and Im(z) = (c) Show there is an expression for the multiplicative inverse of z, the number in terms of just the conjugate 7 and the modulus [z]. (Hint: Refer to (b).)
Transcribed Image Text:2. The set of complex numbers can be defined as the set C = {a + bi | a, b = R, i²=-1}. For any complex number z = a + bi € C, • the real part of z is Re(z) = a and the imaginary part of z is Im(z) = b; the conjugate of z is z = a -bi; and • the modulus of z is |z| = √a² + b². With this notation, answer the following (each can be done in one line of computation). 2+z z-z (a) Show that Re(z) = 2 2i (b) Show that · z = |z|². and Im(z) = (c) Show there is an expression for the multiplicative inverse of z, the number in terms of just the conjugate 7 and the modulus [z]. (Hint: Refer to (b).)
Expert Solution
steps

Step by step

Solved in 5 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS