Explanation Theorem used: De Moivre’s Theorem: If z = r ( cos θ + i sin θ ) and n be a positive integer then, z n = [ r ( cos θ + i sin θ ) ] n = r n ( cos n θ + i sin n θ ) . Calculation: Rewrite the complex number ( 2 3 + 2 i ) in polar form. The polar form of the complex number z = a + b i is z = r ( cos θ + i sin θ ) where r = | z | = a 2 + b 2 and tan θ = b a . Consider the complex number ( 2 3 + 2 i ) . Obtain the argument of the complex number ( 2 3 + 2 i ) . tan θ = 2 2 3 = 1 3 Thus, the argument of argument of the complex number ( 2 3 + 2 i ) is θ = tan − 1 ( 1 3 ) = π 6 Obtain the modulus of the complex number ( 2 3 + 2 i )

Single Variable Calculus: Early Transcendentals, Volume I

8th Edition

ISBN: 9781305270343

Author: James Stewart

Publisher: Cengage Learning

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Chapter H, Problem 35E

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To find: The 5^th power of the complex number (23+2i) by using De Moivre’s Theorem.

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Chapter H Solutions

Single Variable Calculus: Early Transcendentals, Volume I

Ch. H - Prob. 1E Ch. H - Prob. 2E Ch. H - Prob. 3E Ch. H - Prob. 4E Ch. H - Prob. 5E Ch. H - Prob. 6E Ch. H - Prob. 7E Ch. H - Prob. 8E Ch. H - Prob. 9E Ch. H - Prob. 10E

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The 5 th power of the complex number ( 2 3 + 2 i ) by using De Moivre’s Theorem.

Solution Summary: The author explains the 5th power of the complex number (2sqrt3+2i)5 by using De Moivre’s Theorem.

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To find: The 5^th power of the complex number (23+2i) by using De Moivre’s Theorem.

Chapter H Solutions

The 5 th power of the complex number ( 2 3 + 2 i ) by using De Moivre’s Theorem.

Solution Summary: The author explains the 5th power of the complex number (2sqrt3+2i)5 by using De Moivre’s Theorem.

Concept explainers

Videos

To find: The 5th power of the complex number (23+2i) by using De Moivre’s Theorem.

Chapter H Solutions

To find: The 5^th power of the complex number (23+2i) by using De Moivre’s Theorem.