the complex plane; de moivre’s theorem. polar form

The Complex Plane; De Moivre’s Theorem

Upload: theodore-warner

Post on 19-Jan-2016

216 views

Category:

Documents

0 download

Report

Download

Embed Size (px):

TRANSCRIPT

The Complex Plane; De Moivre’s Theorem

)sin(cos

iryixz

Polar Form

1. Plot each complex number in the complex plane and write it in polar

form. Express the argument in degrees

(Similar to p.334 #11-22)

i 1

Page 4: The Complex Plane; De Moivre’s Theorem. Polar Form

2. Plot each complex number in the complex plane and write it in polar

form. Express the argument in degrees

(Similar to p.334 #11-22)

i535

Page 5: The Complex Plane; De Moivre’s Theorem. Polar Form

3. Plot each complex number in the complex plane and write it in polar

form. Express the argument in degrees

(Similar to p.334 #11-22)

Page 6: The Complex Plane; De Moivre’s Theorem. Polar Form

4. Write each complex number in rectangular form

(Similar to p.334 #23-32)

)sin(cos5 i

Page 7: The Complex Plane; De Moivre’s Theorem. Polar Form

5. Write each complex number in rectangular form

(Similar to p.334 #23-32)

6sin

6cos4

Page 8: The Complex Plane; De Moivre’s Theorem. Polar Form

6. Write each complex number in rectangular form

(Similar to p.334 #23-32)

22sin22cos7 i

Page 9: The Complex Plane; De Moivre’s Theorem. Polar Form

21212

21212121

2222

1111

sincos

)sin(cos

irrzz

then

irz

Multiplication and Division

Page 10: The Complex Plane; De Moivre’s Theorem. Polar Form

7. Find zw and z/w. Leave your answers in polar form

(Similar to p.334 #33-40)

120sin120cos

200sin200cos

Page 11: The Complex Plane; De Moivre’s Theorem. Polar Form

8. Find zw and z/w. Leave your answers in polar form

(Similar to p.334 #33-40)

3sin

3cos4

4sin

4cos8

Page 12: The Complex Plane; De Moivre’s Theorem. Polar Form

9. Find zw and z/w. Leave your answers in polar form

(Similar to p.334 #33-40)

Page 13: The Complex Plane; De Moivre’s Theorem. Polar Form

)1(

)sin()cos(

)sin(cos

Theorem sMoivre' De

ninrz

then

irz

Page 14: The Complex Plane; De Moivre’s Theorem. Polar Form

10. Write each expression in the standard form a + bi

(Similar to p.334 #41-52)

4105sin105cos2 i

Page 15: The Complex Plane; De Moivre’s Theorem. Polar Form

11. Write each expression in the standard form a + bi

(Similar to p.334 #41-52)

3sin

3cos2

Page 16: The Complex Plane; De Moivre’s Theorem. Polar Form

Let w = r(cos θo + i sin θo be a complex number, and let n > 2 be an integer. There are n distinct complex nth roots given by:

1,...,2,1,0

2sin

2cos 00

nkwhere

nrz n

Page 17: The Complex Plane; De Moivre’s Theorem. Polar Form

12. Find all the complex roots. Leave your answers in polar form

with the argument in degrees(Similar to p.335 #53-60)

i44 of rootsfourth complex The

Page 18: The Complex Plane; De Moivre’s Theorem. Polar Form

13. Solve the following equation. Leave your answers in polar form

with the argument in degrees(Similar to p.335 #53-60)

275 x

Level 3, 2004 - AHeadStartdownloads.aheadstart.co.nz/Mathematics with... · 3. Few remembered to check for invalid solutions. Candidates found it difficult to use De Moivre’s theorem

POLAR M52 / POLAR M51 POLAR M22 / POLAR M21 … · 61 polar m52™/ polar m51™ polar m22™/ polar m21™ herzfrequenz-messgerÄt gebrauchsanleitung deu

Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem

De Moivre’s Theorem › ... › DeMoivres_Theorem.pdf · De Moivre’s Theorem If n is any integer, (cos θ + i sin θ)n = cos n θ + i sin n θ If n is any fraction, one of the

7.5 Complex Numbers in Polar Form; DeMoivre’s Theorem

Stokes's Theorem, Data, & the Polar Ice Capsghrist/preprints/stokespole.pdf · 2018-04-03 · Stokes's Theorem, Data, & the Polar Ice Caps uliyY Baryshnikov and Robert Ghrist y Abstract

Network Theorems SUPERPOSITION THEOREM THÉVENIN’S THEOREM NORTON’S THEOREM MAXIMUM POWER TRANSFER THEOREM MILLMAN’S THEOREM SUBSTITUTION THEOREM RECIPROCITY

POLAR M52 / POLAR M51 POLAR M22 / POLAR M21 HEART … · 61 polar m52™/ polar m51™ polar m22™/ polar m21™ heart rate monitor user’s manual gbr

COMPARATIVA POLAR V800, POLAR M400 y POLAR RC3

LTD SHEAR BOLTSB46 - Polar Knife Bolt - B46 Knife Bolts for Polar 107, Polar 112, Polar 115, Polar 137, Polar 145, Polar 150 & Polar 155 paper cutters. Socket head cap screw, M12 x

9.4 1920.pdf · 2. From Rectangular (x, y) to Polar (r,O) (Origin) x Pcqar axis (X—axis) Using SOHCAHTOA and the Pythag. Theorem: tano = ex: Convert from rectangular to polar, O

B.Sc./ B.A. I Semestercareercollegeindia.com/career/assets/syllabus... · signs, De Moivre’s theorem and its applications, Direct and inverse circular and hyperbolic functions,

SUCCESSIVE DIFFERENTIATION AND LEIBNITZ’S …...Using De Moivre’s theorem, we get where Example 8 Find the derivative of Solution: Let = where = and = Resolving into partial fractions

anaariguznaga.files.wordpress.com · 8 Complex Vector Spaces 8.1 Complex Numbers 8.2 Conjugates and Division of Complex Numbers 8.3 Polar Form and DeMoivre’s Theorem 8.4 Complex

· Web viewNETWORK THEOREMS : Thevenin’s theorem, Norton’s theorem, superposition theorem, maximum power transfer theorem, Reciprocity theorem, Tellegen’s theorem, Milman's theorem

Oso polar polar-bear

TLFeBOOK - UET Taxilaweb.uettaxila.edu.pk/CMS/teSCms/notes/Satellite_Communications.pdf3.3 The Polar Mount Antenna 75 ... Radio Wave Propagation 91 ... 6.2 Reciprocity Theorem for

Mathematics The Doctrine of Chancesassets.cambridge.org › 97811080 › 61803 › frontmatter › ... · 2013-06-28 · theorem stands as one of de Moivre’s most significant contributions

Tangent Lines and Arc Length for Parametric and Polar … · We can find out some useful information about polar curves that pass through the pole. Theorem. Suppose that the curve

WorkSHEET 8.1 Advanced exponential functions...Maths Quest Maths C Year 12 for Queensland 2e 1 WorkSHEET 8.1 Advanced exponential functions Name: _____ 1 Using de Moivre’s theorem

6.5 Complex Numbers in Polar Form; DeMoivre’s Theorem...Section 6.5 Complex Numbers in Polar Form; DeMoivre’s Theorem 689 By definition, the polar form of is We need to determine

POLAR H7 SENSOR · POLAR H7 SENSOR forrás: zerge.info POLAR S520 POLAR S610 POLAR S710 POLAR S810 POLAR S720 POLAR S725 POLAR S625X POLAR S725X POLAR S725X pro POLAR RS100 POLAR

Complex Numbers in Polar Form and DeMoivres Theorem

€¦ · Web viewNetwork theorems -Superposition theorem, Thevenin’s theorem, Norton’s theorem, Reciprocity theorem, Millman’s theorem, and Maximum power transfer theorem, application

CHAPTER 46 DE MOIVRE’S THEOREM - s3-eu-west … · EXERCISE 195 Page 528 . 1. If. z = x + jy, (a) determine the equation of the locus (b) sketch the locus of the following: z =

Lecture 3 Applications of de Moivre’s theorem Curves … 3 • Applications of de Moivre’s theorem • Curves in the complex plane • Complex functions as mappings

MATHEMATICSsildacscollege.org/wp-content/uploads/2015/07/Math.pdfClassical Algebra Marks: 30 1. Complex numbers: De-Moivre’s theorem and its applications, Exponential, Sine, Cosine

COMPLEX NUMBERS AND DE MOIVRE’S THEOREM€¦ · 39. The conjugate of complex number , 4 2 3 i i − − is (a) 4 3i (b) 17 11 +10 i (c) 17 11 −10 i (d) i i 4 2 +3 40. If z1 and

yvucdc.in · Web viewStatement and proofs of Superposition Theorem, Thevenin's Theorem, Norton's Theorem, Maximum Power transfer theorem, Milliman’s theorem and Reciprocity theorem

Oso polar polar bear

Week 4. Double integrals in polar coordinatessweers/onderwijs/etwi-an/Analysis3Week4.pdf · Week 4. Double integrals to iterated integrals by polar coordinates Fubini’s Theorem

Bearing Complex Polar Coordinates Binomial Theorem (Terms) Trig Equations Law of Cosines Binomial Theorem (Basic) Vectors SSA Triangles Comments Please

DEPARTMENT of PROCESS AUTOMATION … · De Moivre’s Theorem. Matrices. Operations on Matrices. Systems of Linear Equations. Gaussian Method and Cramer’s Rule. The Inverse of a

· Web view• state and use Euler’s formula • state and use De Moivre’s theorem for a rational index • find the roots of a complex number 2.12Functions • define and recognise