11 Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.[5( cos 45° + i sin 45°)³[5( cos 45° + i sin 45°)]3 =(Simplify your answer, including any radicals. Type your answer in the form a + bi. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

The given complex number,5cos 45°+i sin 45°3

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form. [5( cos 45° + i sin 45°)3 ..... [5( cos 45° + i sin 45°)]³ = (Simplify your answer, including any radicals. Type your answer in the form a + bi. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form. [5( cos 45° + i sin 45°)3 ..... [5( cos 45° + i sin 45°)]³ = (Simplify your answer, including any radicals. Type your answer in the form a + bi. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Complex Numbers

Section: Chapter Questions

Problem 18T

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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.
Find the cube roots of 27i, and sketch these roots in the complex plane.

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