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Numbers as Real and Rational, Real and Irrational, or Complex

1. Classify the given numbers as real and rational, real and irrational, or complex.

a. (2)^1/2 + 2

b. i

c. 0

d. 3-(-5)^1/2i

e. (100)^1/5

f. 30007

g. (8)1/3

h. 4+0i

2. Think of any fundamental operation (addition, subtraction, muliplication, division, exponentiation) on

a. Irrational number, which results in:
> A rational number.

> An irrational number.

b. A complex number (a + bi, where a and b are real and b is not equal to zero), which results in:

> A real number.

> A complex number. (a + bi, where a and b are real)

Solution Preview

Welcome! Here you go...

1. Classify the given numbers as real and rational, real and irrational, or complex.

a. (2)^1/2 + 2
real and irrational, since the square root of 2 is irrational

b. i
complex, since 'i' is imaginary

c. 0
real and rational, since you can write it as a fraction: 0/1

d. 3-(-5)^1/2i
complex, since this contains the imaginary ...

Solution Summary

Determining if various numbers are real, rational, complex, etc.

$2.19