#6. Find the square roots of (a) 2i; (b) 1-√3 i and express them in rectangular wordinates. #7. Find the four roots of the equation 2²+4=0 and
#6. Find the square roots of (a) 2i; (b) 1-√3 i and express them in rectangular wordinates. #7. Find the four roots of the equation 2²+4=0 and
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please solve number 6
![#. Reduce each of these quantities to a real number
1+2i
si
3-4 i
(1-2) (2-2) (3-2)
(a)
+
2-2
5 i
(b)
#2. If 2₁ and 2₂ are two complex numbers, show that
12₁-221² + 12₁ +2₂1² = 2 ( 121₁1² + 122 1²).
#3. Assuming either /2/=1 or | w/=1 and ZW 1.
Prove that
Z-W
= 1.
1-ZW
#4. Show that equation | 2-1-2|=1 Can be written as
121²2 Re Z-2 Imz +1=0.
#5. Perform the needed operations.
(a) (1+√3i) 10
(b) (-1+i)7
#6. Find the square roots of (a) 2i; (b) 1-√3 i and
express them in rectangular wordinates.
#7. Find the four roots of the equation Z² +4=0 and
use them to factor z4+4 into quadratic factors with
real wefficients.
#8. In each case, sketch the set of points determined by
the given conditiong
(a) /2-1+2/>1
(b) Re(iz) < -1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeb81122-6fbf-4c63-aaf5-71689ff4fea7%2F6575d5b0-206b-49de-8f75-e6cf01ae5cc9%2Fd4v7z7_processed.png&w=3840&q=75)
Transcribed Image Text:#. Reduce each of these quantities to a real number
1+2i
si
3-4 i
(1-2) (2-2) (3-2)
(a)
+
2-2
5 i
(b)
#2. If 2₁ and 2₂ are two complex numbers, show that
12₁-221² + 12₁ +2₂1² = 2 ( 121₁1² + 122 1²).
#3. Assuming either /2/=1 or | w/=1 and ZW 1.
Prove that
Z-W
= 1.
1-ZW
#4. Show that equation | 2-1-2|=1 Can be written as
121²2 Re Z-2 Imz +1=0.
#5. Perform the needed operations.
(a) (1+√3i) 10
(b) (-1+i)7
#6. Find the square roots of (a) 2i; (b) 1-√3 i and
express them in rectangular wordinates.
#7. Find the four roots of the equation Z² +4=0 and
use them to factor z4+4 into quadratic factors with
real wefficients.
#8. In each case, sketch the set of points determined by
the given conditiong
(a) /2-1+2/>1
(b) Re(iz) < -1.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 4 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)