document.write( "Question 594347: classify the given numbers as real and rational, real and irrational, or complex\r
\n" ); document.write( "\n" ); document.write( "(4)^1/2 + 2 \n" ); document.write( "

Algebra.Com's Answer #376703 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
First we'll simplify the expression. Then we will determine the class(es) of the number.

\n" ); document.write( "Since 1/2 as an exponent means square root and since the square root of 4 is 2, this expression simplifies as follows:
\n" ); document.write( " $\"4%5E%281%2F2%29+%2B+2+=+2+%2B+2+=+4\"$

\n" ); document.write( "Complex numbers are two-part numbers: a real part and an imaginary part. They are written in the form: a + bi where \"a\" is the real part of the complex number and \"bi\" is the imaginary part of the complex number. The \"i\" is the name for $\"sqrt%28-1%29\"$ and the \"a\" and \"b\" can be any real number.

\n" ); document.write( "Every number I know of is a complex number! IOW there are NO numbers that are not complex. Simple numbers like 10 are just complex numbers whose imaginary parts are zero: 10 + 0i

\n" ); document.write( "But the phrasing of your question, \"real and rational, real and irrational, or complex\". makes me think that complex numbers are considered a separate class of numbers from the other two. So I am going to answer your question two ways: the correct way and the way that considers complex numbers to be separate from the other two classes.

\n" ); document.write( "Correct:

4 is complex because it can be written as 4 + 0i and the 4 and the 0 are real numbers.
4 is real because the imaginary part of 4 + 0i is zero.
4 is rational because it can be written as the ratio of two integers: 4 = 4/1.
So the correct answer is that 4 is complex, real and rational (all three).

\n" ); document.write( "If it is believed (incorrectly) that complex numbers must have a non-zero imaginary part, then 4 is just real and rational. \n" ); document.write( "

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