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3) Show that (a + bi)º = (a – bi). Hint: for any x, y in a field containing Fp, (x+y)º = xº + yP. %3D

3) Show that (a + bi)º = (a – bi). Hint: for any x, y in a field containing Fp, (x+y)º = xº + yP. %3D

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 13E
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(3) Show that (a + bi)P = (a – bi). Hint: for any x, y in a field containing Fp, (x + y)P = xP + yP. %3D (4) The norm of an element a + bi in F,[i] is N(a + bi) = (a + bi)(a – bi) = a² + b² e F, Show that for r, y e Fp[i], N(xy) = N (x)N(y). (5) Deduce from (3) that N(a + bi) = (a + bi)P+l 1
Transcribed Image Text:(3) Show that (a + bi)P = (a – bi). Hint: for any x, y in a field containing Fp, (x + y)P = xP + yP. %3D (4) The norm of an element a + bi in F,[i] is N(a + bi) = (a + bi)(a – bi) = a² + b² e F, Show that for r, y e Fp[i], N(xy) = N (x)N(y). (5) Deduce from (3) that N(a + bi) = (a + bi)P+l 1
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