Questions on Algebra: Real numbers, Irrational numbers, etc answered by real tutors!

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Question 152070This question is from textbook elementary and intermediate algebra concepts and applications
: I'm not sure how to do these can I please get help?


2. a) Select any irrational number, and turn it into a rational number by
using addition, subtraction, multiplication, division, or exponentiation.
b) Select any imaginary number (of the form "a + bi" where a and b are non-zero real numbers), and turn it into a real number by using addition, subtraction, multiplication, division, or exponentiation.
This question is from textbook elementary and intermediate algebra concepts and applications
: I'm not sure how to do these can I please get help?


2. a) Select any irrational number, and turn it into a rational number by
using addition, subtraction, multiplication, division, or exponentiation.
b) Select any imaginary number (of the form "a + bi" where a and b are non-zero real numbers), and turn it into a real number by using addition, subtraction, multiplication, division, or exponentiation.

Answer by orca(336) About Me  (Show Source):
You can put this solution on YOUR website!
a)
choose an arbitrary irrational number, say
3+sqrt(2)
To turn it into a rational number, we simply multiply it by
3-sqrt(2)
The result is
(3+sqrt(2))(3-sqrt(2))=3^2-(sqrt(2))^2=9-2 =7
b)
choose an imaginary irrational number, say
2+i
To turn it into an imaginary number, we simply multiply it by
2-i
The result is
(2+i)(2-i)=2^2-i^2=4-(-1)=4+1=5