pls show full sol, thanks [MO41] Solve the following complex number problems. Solutions for complex numbertransformation is required in this item.5eiC.2e0.25πί_e-πί(Express your answer in rectangular form)

The expression 5ei2e0.25πi-e-πi is given. Use the formula reit=r ( cos t+ i sin t)

Answered: 5ei C. 2e0.25πί-e- πί (Express your…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Complex Numbers

Section: Chapter Questions

Problem 7T

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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.
Recall from the introduction to Section 8.2 that Jerome Cardans solutions to the equation x3=15x+4 could be written as x=2+11i3+211i3 Lets assume that the two cube roots are complex conjugates. If they are, then we can simplify our work by noticing that x=2+11i3+211i3=a+bi+abi=2a which means that we simply double the real part of each cube root of 2+11i to find the solutions to x3=15x+4. Now, to end our work with Cardan, find the three cube roots of 2+11i. Then, noting the discussion above, use the three cube roots to solve the equation x3=15x+4. Write your answers accurate to the nearest thousandth.

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5ei C. 2e0.25πί-e- πί (Express your answer in rectangular form)