10. In the Argand diagram on the right, OABC is a rectangle, withOC = 20A. The vertex A corresponds to the complex number w.(a) What complex number corresponds to the vertex C?(b) What complex number corresponds to the point of intersectionD of the diagonals OB and AC?B ^yCA(@)

Given: The figure- OABC is a rectangle. OC=2OA The vertex A corresponds to the complex number ω…

Answered: 10. In the Argand diagram on the right,…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.CR: Chapter Review

Problem 4CC

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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) = ________________.
Plot z=34i in the complex plane and find its absolute value.
Fractals Complex numbers are fundamental in the creation of the intricate geometric shape shown below, called a fractal. The process of creating this image is based on the following sequence of steps, which begins by picking any complex number, which we will call z. 1. Square z, and then add that result to z. 2. Square the result from step1, and then add it to z. 3. Square the result from step2, and then add it to z. If we begin with the complex number i, what is the result after performing steps 1, 2 and 3?

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10. In the Argand diagram on the right, OABC is a rectangle, with OC = 20A. The vertex A corresponds to the complex number w. (a) What complex number corresponds to the vertex C? (b) What complex number corresponds to the point of intersection D of the diagonals OB and AC? В У A(@)