Explanation Given information: [ c i s 18 ° ] 10 Concept Involved: We use de Moivre’s Theorem to find powers of complex numbers written in trigonometric form. If z = r ( cos θ + i sin θ ) = r c i s θ is a complex number in trigonometric form and n is an integer, then z n = [ r ( cos θ + i sin θ ) ] n = r n ( cos n θ + i sin n θ ) = r n c i s n θ To find the nth power of a complex number, find the nth power of moduli and multiply the arguments by nth power Modulus: The absolute value or modulus of the complex number z = x + y i is the distance from the origin to the point ( x , y ) in the complex plane. If this distance is denoted by r , then r = | z | = | x + y i | = x 2 + y 2 Argument: The argument of the complex number z = x + y i , denoted a r g ( z ) , is the smallest positive angle θ from the positive real axis to the graph of z. Trigonometric Form: If z = x + y i is a complex number in standard form, then the trigonometric form of z is given by: z = r ( cos θ + i sin θ ) = r c i s θ Where r is the modulus of z and θ is the argument of z. We can convert back and forth between standard form and trigonometric form using the relationships that follow: For z = x + y i = r ( cos θ + i sin θ ) = r c i s θ r = x 2 + y 2 and θ is such that cos θ = x r , sin θ = y r , a n d tan θ = y x The sign of trigonometric ratio in different quadrants

Bundle: Trigonometry, Loose-leaf Version, 8th + MindTap Math, 1 term (6 months) Printed Access Card

8th Edition

ISBN: 9781337131063

Author: Charles P. McKeague, Mark D. Turner

Publisher: Cengage Learning

See similar textbooks

Question

Chapter 8.3, Problem 28PS

To determine

To find:

The standard form of the given expression using de Moivre’s Theorem

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.3, Problem 27PS

Chapter 8.3, Problem 29PS

Students have asked these similar questions

Was ist eine Transormation im Bezug zum Thema Trigonometrie?

the point (1,4) is on the graph of y=f(x). Determine the co-ordinates of the image of this point on the graph of y=3f (-4(x+1))-2 I have just asked this question but the response still did not make sense. Please can you give me a step by step and why to this question. thank you

T3.2: Prove that if the Graceful Tree Conjecture (every tree has a graceful labeling) is true and T' is a tree with m edges, then K2, decomposes into 2m - 1 copies of T. Hint - Delete a leaf to get 7" and apply the decomposition of K2(m-1)+1 = K2m-1 into T'. Then explain how the decomposition allows the pendant edge to be added to a new vertex to obtain a decomposition of K2m into copies of T.

Chapter 8 Solutions

Bundle: Trigonometry, Loose-leaf Version, 8th + MindTap Math, 1 term (6 months) Printed Access Card

Ch. 8.1 - For Questions 1 through 10, fill in the blank with...Ch. 8.1 - Prob. 2PS Ch. 8.1 - Prob. 3PS Ch. 8.1 - Prob. 4PS Ch. 8.1 - Prob. 5PS Ch. 8.1 - Prob. 6PS Ch. 8.1 - Prob. 7PS Ch. 8.1 - Prob. 8PS Ch. 8.1 - Prob. 9PS Ch. 8.1 - Prob. 10PS

Knowledge Booster

The standard form of the given expression using de Moivre’s Theorem

Solution Summary: The author explains how they use de Moivre's Theorem to find the nth power of complex numbers written in trigonometric form.

To find: The standard form of the given expression using de Moivre’s Theorem

Want to see the full answer?

Chapter 8 Solutions

To find:

The standard form of the given expression using de Moivre’s Theorem