SOLUTION: 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,

Algebra ->  Real-numbers -> SOLUTION: 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,      Log On


   

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

Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
a)
choose an arbitrary irrational number, say
3%2Bsqrt%282%29
To turn it into a rational number, we simply multiply it by
3-sqrt%282%29
The result is
%283%2Bsqrt%282%29%29%283-sqrt%282%29%29=3%5E2-%28sqrt%282%29%29%5E2=9-2+=7
b)
choose an imaginary irrational number, say
2%2Bi
To turn it into an imaginary number, we simply multiply it by
2-i
The result is
%282%2Bi%29%282-i%29=2%5E2-i%5E2=4-%28-1%29=4%2B1=5