11. The vertices of an equilateral triangle are equidistant from the origin. One of its verticesis at 1+ V3i. Find the complex numbers represented by the other two vertices.[HINT: What is the angle subtended by the vertices at the origin?]

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Answered: 11. The vertices of an equilateral…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 35E

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Similar questions

The diagram shown in Figure 1 was used by the Hindu mathematician Bhaskara to prove the theorem in the 12th century. His proof consisted only of the diagram and the word Behold! Use this figure to derive the Pythagorean Theorem. The right triangle with sides a, b, and c has been repeated three times. The area of the large square is equal to the sum of the areas of the four triangles and the area of the small square in the center. The key to this derivation is in finding the length of a side of the small square. Once you have the equation, simplify the right side to obtain the theorem. Figure 1
(a) The complex conjugate of 3+4i is 3+4i = ______________. (b) (3+4i)(3+4i) = ________________.
Prove that for complex numbers .
As was mentioned in the introduction to this chapter, Jerome Cardan (Girolamo Cardano) was unable to solve certain equations because he did not know how to interpret the square root of a negative number. His work set the stage for thc arrival of complex numbers Research the history of complex numbers. How were the works of Rafael Bombelli, Jean Robert Argand, Lconhard Euler, and Abraham de Moivre significant in the development of complex numbers? Write a paragraph or to about your findings.
Prove that the altitude drawn to the hypotenuse of a right triangle separates the right triangle into two right triangles that are similar to each other and to the original right triangle.

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11. The vertices of an equilateral triangle are equidistant from the origin. One of its vertices is at 1+ V3i. Find the complex numbers represented by the other two vertices. [HINT: What is the angle subtended by the vertices at the origin?]