Answered: Write down monic polynomials in R[X] of…

Write down monic polynomials in R[X] of least possible degree which have the following complex numbers as roots: −2 and 5 + 3i; 1 + i and 3i; 5 and −√7.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 40E

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Question

Write down monic polynomials in R[X] of least possible degree which have the following complex numbers as roots:
−2 and 5 + 3i;
1 + i and 3i;
5 and −√7.

Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.

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