Let a be a complex number that is algebraic over Q and let r be arational number. Show that ar is algebraic over Q.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.2: Ring Homomorphisms
Problem 15E: In the field of a complex numbers, show that the mapping that maps each complex number onto its...
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Let a be a complex number that is algebraic over Q and let r be a
rational number. Show that ar is algebraic over Q.

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