Part 1: X=345.218 Y=2A2.b16 Z-101101011.11012 W=3.14 Calculate: Y*Z-X*W correct to 3 octal places in the octal system (Show all steps) Part 2: The complex quadratic function: f(z)=z²+az+ b has 2 roots: Z₁=3+4i and Z2=12-5 i 1. Calculate Re(a), Im(a), Re(b), Im(b) 2. arg(z₁/Z2), |Z1Z2l, 3. √/2₁/22 4. (BONUS): |z₁22| (find all 3 roots in polar representation) (4 significant figures) Part 3: 1. Given: x= cos(0); prove that Theorem) examine the similar problem: x= sin(0) .. sin(50) = (x-polynomial) 2. Calculate an approximation of cos(12º) using a suitable de Moivre's formula (use Newton Raphson, 4 steps and compare your result with the correct value) cos(50) = 5x20x³ + 16x5 (Use de Moivre's

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Part 1:
X=345.218
Y=2A2.b16
|Z=101101011.1101₂
W=3.14
Calculate: Y*Z-X*W correct to 3 octal places in the octal system (Show all steps)
Part 2:
The complex quadratic function:
f(z)=z²+az+ b
has 2 roots: Z₁=3+4i and Z2-12-5i
1. Calculate Re(a), Im(a), Re(b), Im(b)
2. arg(z₁/Z2), |Z1Z2l,
3. √/2₁/22
4. (BONUS): |z₁²2|
(find all 3 roots in polar representation)
(4 significant figures)
Part 3:
1. Given: x= cos(0); prove that
Theorem)
cos(50) = 5x20x³ + 16x5
(Use de Moivre's
examine the similar problem: x= sin(0) ..sin(50) =
(x-polynomial)
2. Calculate an approximation of cos(12º) using a suitable de Moivre's formula (use Newton
Raphson, 4 steps and compare your result with the correct value)
Transcribed Image Text:Part 1: X=345.218 Y=2A2.b16 |Z=101101011.1101₂ W=3.14 Calculate: Y*Z-X*W correct to 3 octal places in the octal system (Show all steps) Part 2: The complex quadratic function: f(z)=z²+az+ b has 2 roots: Z₁=3+4i and Z2-12-5i 1. Calculate Re(a), Im(a), Re(b), Im(b) 2. arg(z₁/Z2), |Z1Z2l, 3. √/2₁/22 4. (BONUS): |z₁²2| (find all 3 roots in polar representation) (4 significant figures) Part 3: 1. Given: x= cos(0); prove that Theorem) cos(50) = 5x20x³ + 16x5 (Use de Moivre's examine the similar problem: x= sin(0) ..sin(50) = (x-polynomial) 2. Calculate an approximation of cos(12º) using a suitable de Moivre's formula (use Newton Raphson, 4 steps and compare your result with the correct value)
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,