SOLUTION: classify the given numbers as real and rational, real and irrational, or complex (4)^1/2 + 2

Question 594347: classify the given numbers as real and rational, real and irrational, or complex
(4)^1/2 + 2
Found 2 solutions by jsmallt9, richard1234:
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First we'll simplify the expression. Then we will determine the class(es) of the number.

Since 1/2 as an exponent means square root and since the square root of 4 is 2, this expression simplifies as follows:

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 and the "a" and "b" can be any real number.

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

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.

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).

If it is believed (incorrectly) that complex numbers must have a non-zero imaginary part, then 4 is just real and rational.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
4^(1/2) + 2 = 4

4 is real and rational. Technically it is also considered complex because it can be plotted on the complex plane.
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