Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Question 1 (a) Express the following in real-imaginary form: 2i(1 – i) + (V3 + 1)° + (1 + i)(I+,i). (b) Let z = 4- 2i and w = 3+5i. Express z2/w in real-imaginary form. (c) Let z = 2- 2i and w-1-3i. Plot z, w and z on the complex plane.

Question 1 (a) Express the following in real-imaginary form: 2i(1 – i) + (V3 + 1)° + (1 + i)(I+,i). (b) Let z = 4- 2i and w = 3+5i. Express z2/w in real-imaginary form. (c) Let z = 2- 2i and w-1-3i. Plot z, w and z on the complex plane.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 35E
See similar textbooks
icon
Related questions
Question
Question 1 (a) Express the following in real-imaginary form: 2i(1 – i) + (V3 + 1)? + (1+ i)(I +i). (b) Let z = 4 - 2i and w = 3+5i. Express z2/w in real-imaginary form. (c) Let z = 2– 2i and w = -1-3i. Plot z, w and z on the complex plane. Question 2 Let p(z) = z° – 2* + 10z° + 82? – 16z + 80. (a) Given that z - 1 – 3i is a factor of p(z), factorize p(z) into quadratic and cubic factors. (b) Find the cube roots of -8 in mod-arg form. (c) Hence factorize p(2) into linear factors. (You may leave complex numbers in mod-arg form if you wish.) Question 3 Find the sum to infinity of sin 0 + } sin 40 + į sin 70 + ... Hint: the formula for the sum of a geometric series is in the info shect. Question 4 (a) Evaluate In(-3- /3i), and sketch the values on the Complex Plane. Which is the principal value? (b) Use the definition of 2" to show that i' is always pure real. (c) Use the definition sin z = (e" -e-") to express sin z in real-imaginary form. (d) Express Im(e(z+tv)) in terms of z and y.
Transcribed Image Text:Question 1 (a) Express the following in real-imaginary form: 2i(1 – i) + (V3 + 1)? + (1+ i)(I +i). (b) Let z = 4 - 2i and w = 3+5i. Express z2/w in real-imaginary form. (c) Let z = 2– 2i and w = -1-3i. Plot z, w and z on the complex plane. Question 2 Let p(z) = z° – 2* + 10z° + 82? – 16z + 80. (a) Given that z - 1 – 3i is a factor of p(z), factorize p(z) into quadratic and cubic factors. (b) Find the cube roots of -8 in mod-arg form. (c) Hence factorize p(2) into linear factors. (You may leave complex numbers in mod-arg form if you wish.) Question 3 Find the sum to infinity of sin 0 + } sin 40 + į sin 70 + ... Hint: the formula for the sum of a geometric series is in the info shect. Question 4 (a) Evaluate In(-3- /3i), and sketch the values on the Complex Plane. Which is the principal value? (b) Use the definition of 2" to show that i' is always pure real. (c) Use the definition sin z = (e" -e-") to express sin z in real-imaginary form. (d) Express Im(e(z+tv)) in terms of z and y.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS