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QuestionWhich set does not include (i3)2(i \sqrt{3})^{2}? Choose one: a. Complex b. Imaginary c. Rational d. Integers

Studdy Solution

STEP 1

Assumptions1. We are asked to find which set of numbers does not contain the value of (i3)(i \sqrt{3})^{}. . The sets of numbers given are Complex Numbers, Pure Imaginary Numbers, Rational Numbers, and Integers.
3. The symbol ii represents the imaginary unit, which is defined by its property i=−1i^{} = -1.

STEP 2

First, we need to calculate the value of (i)2(i \sqrt{})^{2}.
(i)2(i \sqrt{})^{2}

STEP 3

Apply the power rule, which states that (am)n=amn(a^{m})^{n} = a^{mn}, to the expression.
(i3)2=i2×(3)2(i \sqrt{3})^{2} = i^{2} \times (\sqrt{3})^{2}

STEP 4

Calculate the value of i2i^{2} and (3)2(\sqrt{3})^{2}.
i2=−1,(3)2=3i^{2} = -1, \quad (\sqrt{3})^{2} =3So, the expression becomes−1×3-1 \times3

STEP 5

Calculate the value of −1×3-1 \times3.
−1×3=−3-1 \times3 = -3

STEP 6

Now that we have the value of (i3)2(i \sqrt{3})^{2}, we can determine which set of numbers does not contain this value.
The value −3-3 is a negative integer, so it belongs to the set of Integers.
The value −3-3 is also a rational number, as it can be expressed as a ratio of two integers, so it belongs to the set of Rational Numbers.
The value −3-3 is also a complex number, as all real numbers (including integers and rational numbers) are a subset of complex numbers, so it belongs to the set of Complex Numbers.
However, the value −3-3 is not a pure imaginary number, as it does not have an imaginary part.
Therefore, the set of numbers that does not contain the value of (i3)2(i \sqrt{3})^{2} is the set of Pure Imaginary Numbers.

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