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GRE Subject Test: Math : Operations on Complex Numbers

Study concepts, example questions & explanations for GRE Subject Test: Math

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All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #281 : Gre Subject Test: Math

$\sqrt{-70}\cdot -\sqrt{-50}$

Possible Answers:

$10\sqrt{30}$

$10\sqrt{35}$

$5\sqrt{10}$

$-5\sqrt{5}$

$5\sqrt{20}$

Correct answer:

$10\sqrt{35}$

Explanation:

$\sqrt{-70}\cdot -\sqrt{-50}$

Take out i (the square root of -1) from both radicals, simplify, and then multiply. You are not allowed to first multiply the radicals and then simplify because the roots are negative.

$i\sqrt{70}\cdot -i\sqrt{50}$

$i\sqrt{70}\cdot -i\sqrt{25\cdot 2}$

$i\sqrt{70}\cdot -5i\sqrt{2}$

$-5i^{2}\sqrt{140}$

$-5(-1)\sqrt{140}$

$5\sqrt{140}$

$5\sqrt{4\cdot 35}$

$10\sqrt{35}$

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Example Question #31 : Imaginary Numbers & Complex Functions

$\sqrt{-225}\cdot \sqrt{-289}$

Possible Answers:

25i

255i

$-15\sqrt{17}$

$15i\sqrt{17}$

Correct answer:

Explanation:

$\sqrt{-225}\cdot \sqrt{-289}$

Take out i (the square root of -1) from both radicals, simplify, and then multiply. You are not allowed to first multiply the radicals and then simplify because the roots are negative.

$i\sqrt{225}\cdot i\sqrt{289}$

$15i\cdot 17i$

$255i^{2}$

255(-1)

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Example Question #91 : Algebra

$\sqrt{-15}\cdot \sqrt{-33}$

Possible Answers:

$-3\sqrt{55}$

$-i\sqrt{495}$

$i\sqrt{495}$

$-\sqrt{495}$

$\sqrt{495}$

Correct answer:

$-3\sqrt{55}$

Explanation:

$\sqrt{-15}\cdot \sqrt{-33}$

Take out i (the square root of -1) from both radicals and then multiply. You are not allowed to first multiply the radicals and then simplify because the roots are negative.

$i\sqrt{15}\cdot i\sqrt{33}$

$i^{2}\sqrt{495}$

$(-1)\sqrt{495}$

It might be difficult to tell that this simplifies but you should always check if the perfect squares (4, 9, 16, etc) divide into this number. 9 does divide into 495 so this simplifies further.

$-\sqrt{9\cdot 55}$

$-3\sqrt{55}$

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Example Question #281 : Gre Subject Test: Math

$-\sqrt{121}\cdot \sqrt{-12}$

Possible Answers:

$-44\sqrt{3}$

$-22i\sqrt{3}$

$44i\sqrt{3}$

$-44i\sqrt{3}$

$11i\sqrt{12}$

Correct answer:

$-22i\sqrt{3}$

Explanation:

$-\sqrt{121}\cdot \sqrt{-12}$

Take out i (the square root of -1) from the radical, simplify each radical, then multiply.

$-\sqrt{121}\cdot i\sqrt{12}$

$-11\cdot i\sqrt{4\cdot 3}$

$-11\cdot 2i\sqrt{3}$

$-22i\sqrt{3}$

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GRE Subject Test: Math : Operations on Complex Numbers

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #281 : Gre Subject Test: Math

Example Question #31 : Imaginary Numbers & Complex Functions

Example Question #91 : Algebra

Example Question #281 : Gre Subject Test: Math

All GRE Subject Test: Math Resources

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