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All Common Core: High School - Number and Quantity Resources

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Flashcards: The Complex Number System

Simplifying the following.

$\sqrt{-9}\times\sqrt{18}$

$9i^2\sqrt{2}$

$9i\sqrt{2}$

$-9i\sqrt{2}$

$9\sqrt{2}$

$-9\sqrt{2}$

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Flashcards: The Complex Number System

Simplifying the following.

$\sqrt{-9}\times\sqrt{18}$

Your answer:

$9i^2\sqrt{2}$

Your answer:

$-9i\sqrt{2}$

Your answer:

$9\sqrt{2}$

Your answer:

$-9\sqrt{2}$

Correct answer:

$9i\sqrt{2}$

Explanation:

This question tests one's ability to perform arithmetic operations on complex numbers. Questions like this introduces and builds on the concept of complex numbers. Recall that a complex number by definition contains a negative square. In mathematical terms this is expressed as follows.

$\\i=\sqrt{-1} \\i^2=-1$

Performing arithmetic operations on complex numbers relies on the understanding of the various algebraic operations and properties (distributive, associative, and commutative properties) as well as the imaginary, complex number .

For the purpose of Common Core Standards, "know there is a complex number such that i^2=-1 , and every complex number has a form a+bi with and are reals", falls within the Cluster A of "perform arithmetic operations with complex numbers" (CCSS.MATH.CONTENT.HSF.CN.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Perform multiplication between the two terms.

$\sqrt{-9}\times\sqrt{18}$

Recall that multiplication between two radicand terms (terms under the square root sign), can be combined as one using the communicative property with multiplication.

$\\ \sqrt{a}\times \sqrt{b}=\sqrt{a\times b} \\ \sqrt{-9}\times\sqrt{18}=\sqrt{-9\times 18}$

Step 2: Factor the two term in the expression.

$\\=\sqrt{-9\times 18} \\=\sqrt{-1\times 9\times 9\times 2}$

Step 3: Pull out common terms that exists in the radicand.

Remember that when a number appears under the square root sign, one of the numbers can be brought out front and the other one is canceled out.

$\sqrt{a\times a}= a\sqrt{1}=a$

$\\=\sqrt{-1\times 9\times 9\times 2} \\=9\sqrt{-1\times 2}$

Step 4: Use the identity that $\sqrt{-1}=i$ .

$\\=9\sqrt{-1\times 2} \\=9i\sqrt{2}$

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All Common Core: High School - Number and Quantity Resources

Flashcards: The Complex Number System

Flashcards: The Complex Number System

Flashcards: The Complex Number System

Flashcards: The Complex Number System

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All Common Core: High School - Number and Quantity Resources

Flashcards: The Complex Number System

Flashcards: The Complex Number System

Flashcards: The Complex Number System

Flashcards: The Complex Number System

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