SOLVE STEP BY STEP IN DIGITAL FORMAT4. Show that any complex number of norm 1 (except -1) can be written in the form z = (1 + it)/(1 - it) for some t E R.

We have to prove that any complex number of norm 1 (except -1) can be written in the form…

Answered: 4. Show that any complex number of norm…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter1: Equations And Inequalities

Section1.3: Complex Numbers

Problem 109E

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Similar questions

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.
Determine the number and nature of the roots of the equation in Exercise 67. Calculate the discriminant associated with the equation 6x2+5x+1=0.

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4. Show that any complex number of norm 1 (except -1) can be written in the form z = (1 + it)/(1 − it) for some t E R.