1-10iQ2. If complex number z satisfies the equation: 2z – 57 =3 – iwhere z denotes the complexconjugate of z . Then solve the equation, giving the answer in the form x + iy.

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Answered: 1-10i Q2. If complex number z satisfies…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.6: De Moivre’s Theorem And Nth Roots Of Complex Numbers

Problem 12E

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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.
(a) The complex conjugate of 3+4i is 3+4i = ______________. (b) (3+4i)(3+4i) = ________________.
For the complex number 3+4i real part is ______________, and the imaginary part is _______________.
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.

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1-10i Q2. If complex number z satisfies the equation: _2z – 57 = 3 – i where z denotes the complex conjugate of z. Then solve the equation, giving the answer in the form x + iy.