Numbers as Real and Rational, Real and Irrational, or Complex
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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)
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Solution Summary
Determining if various numbers are real, rational, complex, etc.
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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 ...
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