Explanation Given Information: The equation x 3 − ( 1 − i 3 ) = 0 . Formula used: Demoivre’s Theorem r = z k n z k = r n [ cos ( θ + 360 ° k n ) + i sin ( θ + 360 ° k n ) ] Calculation: Solution of equation in complex number system can be found by application of Demoivre’s Theorem. Demoivre’s Theorem for finding complex roots states that every complex number has two distinct complex square roots, three distinct complex cube roots, four distinct complex fourth roots, and so on. Each root has the same modulus. r = z k n z k = r n [ cos ( θ + 360 ° k n ) + i sin ( θ + 360 ° k n ) ] Here k is the number of distinct n t h solution and θ is in degree. There are exactly three solutions of provided equation as degree of equation is 3 . x 3 = ( 1 − 3 i ) x 3 3 = 1 − 3 i 3 x = 1 − 3 i 3 = 2 ( cos 300 ° + i sin 300 ° ) 3 Apply Demoivre’s Theorem to find all solutions of provided equation. Here, n = 3 as number of solutions is three. z k = 2 3 [ cos ( 300 ° + 360 ° k 3 ) + i sin ( 300 ° + 360 ° k 3 ) ] Here, k = 0 , 1 , 2 . Insert above values of k to find three distinct solution of provided equation. For k = 0 z 0 = 2 3 [ cos ( 300 ° + 360 ° ⋅ ( 0 ) 3 ) + i sin ( 300 ° + 360 ° ⋅ ( 0 ) 3 ) ] = 2 3 [ cos 100 ° + i sin 100 ° ] Above solution is in the polar form

6th Edition

ISBN: 8220103679510

Author: Blitzer

Publisher: PEARSON

See similar textbooks

Concept explainers

Quadratic Equation

When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations …

Demand and Supply Function

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to …

Videos

Question

Chapter 6.5, Problem 86PE

To determine

To calculate: Thesolution of x3−(1−i3)=0 in complex number system. Express solution in polar and rectangular form.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.5, Problem 85PE

Chapter 6.5, Problem 87PE

Students have asked these similar questions

i need help please

(#1) Consider the solid bounded below by z = x² and above by z = 4-y². If we were to project this solid down onto the xy-plane, you should be able to use algebra to determine the 2D region R in the xy-plane for the purposes of integration. Which ONE of these limite of integration would correctly describe R? (a) y: x24x: -22 - (b) y: 22 x: 04-y² (c) y: -√√4-x2. →√√4x²x: −2 → 2 (d) z: 24-y² y: -2 → 2 (e) None of the above

X MindTap - Cenxxxx Answered: tat "X A 26308049 X 10 EKU-- SP 25: X E DNA Sequenc X b/ui/evo/index.html?elSBN=9780357038406&id=339416021&snapshotid=877369& GE MINDTAP , Limits, and the Derivative 40. Answer 5 4-5 t-10 5 f(x) = 2x - 4 if x ≤0 if x 0 10 ++ -4-3-2-1 f(x) = MacBook Pro Search or type URL 5 1234 x² +1 if x = 0 if x = 0 +

Chapter 6 Solutions

EBK PRECALCULUS

Ch. 6.1 - Check Point 1 Solve the triangle shown in Figure...Ch. 6.1 - Check Point 2 Solve triangle ABC if A=40,C=22.5,...Ch. 6.1 - Check Point 3 Solve triangle ABC if A = 57 a = 33,...Ch. 6.1 - Check Point 4 Solve triangle ABC if A = 50, a =...Ch. 6.1 - Prob. 5CP Ch. 6.1 - Check Point 6 Find the area of a triangle having...Ch. 6.1 - Check Point 7 Two fire-lookout stations are 13...Ch. 6.1 - Prob. 1CVC Ch. 6.1 - Prob. 2CVC Ch. 6.1 - Prob. 3CVC

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Thesolution of x 3 − ( 1 − i 3 ) = 0 in complex number system. Express solution in polar and rectangular form.

Solution Summary: The author explains how the solution of equation in complex number system can be found by application of Demoivre’s Theorem.

Concept explainers

Videos

To calculate: Thesolution of x3−(1−i3)=0 in complex number system. Express solution in polar and rectangular form.

Want to see the full answer?

Chapter 6 Solutions