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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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Example Questions

Example Question #11 : Operations On Complex Numbers

Simplify: (4-7i)(1-2i)

Possible Answers:

-10-15i

4-15i+14i^2

5-9i

4-14i

Correct answer:

-10-15i

Explanation:

$In\ order\ to\ simplify\ (4-7i)(1-2i)\ we\ must\ multiply\ the\ binomials\ using\ the\ FOIL\ method.$

$F\ is\ for\ first\ times\ first: =4*1=4$

$O\ is\ for\ outside\ times\ outside =4*(-2i)=-8i$

$I\ is\ for\ inside\ times\ inside=(-7i)*1=-7i$

$L\ is\ for\ last\ times\ last =(-7i)*(-2i)=14i^2$

$Now\ we\ combine\ like\ terms\ and\ simplify:$

4-8i-7i+14i^2

$^* Remember\ that\ i^2=-1$

4-15i+14(-1)=-10-15i

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Example Question #12 : Operations On Complex Numbers

Simplify: (5-8i)^2

Possible Answers:

25-64i

-39-80i

25-64i^2

Correct answer:

-39-80i

Explanation:

$When\ a\ binomial\ is\ squared\ we\ must\ write\ it\ out\ twice\ and\ perform\ the\ FOIL\ method.$

(5-8i)^2=(5-8i)(5-8i)

$F\ is\ for\ first\ times\ first = 5*5=25$

$O\ is\ for\ outside\ times\ outside = 5*8i=40i$

$I\ is\ for\ inside\ times\ inside: 8i*5=40i$

$L\ is\ for\ last\ times\ last = 8i*8i=64i^2=64(-1)=-64$

Now we put each of these together and combine like terms:

25-40i-40i-64=-39-80i

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Example Question #21 : Imaginary Numbers & Complex Functions

$\frac{\sqrt{-16}}{\sqrt{-8}}$

Possible Answers:

$-\sqrt{2}$

$\sqrt{2}$

Correct answer:

$\sqrt{2}$

Explanation:

$\frac{\sqrt{-16}}{\sqrt{-8}}$

Take i (the square root of -1) out of both radicals then divide.

$\frac{i\sqrt{16}}{i\sqrt{8}}$

$\frac{\sqrt{16}}{\sqrt{8}}$

$\sqrt{2}$

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Example Question #81 : Classifying Algebraic Functions

$\sqrt{-16}\cdot \sqrt{-25}$

Possible Answers:

20i

$4\sqrt{5}$

40i

Correct answer:

Explanation:

$\sqrt{-16}\cdot \sqrt{-25}$

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.

$4i\cdot 5i$

$20i^{2}$

Make i squared -1

20(-1)

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Example Question #91 : Algebra

$\sqrt{-7}\cdot \sqrt{-4}$

Possible Answers:

$i\sqrt{28}$

$2\sqrt{7}$

$-2\sqrt{7}$

$-i\sqrt{7}$

$\sqrt{28}$

Correct answer:

$-2\sqrt{7}$

Explanation:

$\sqrt{-7}\cdot \sqrt{-4}$

First, 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.

$i\sqrt{7}\cdot 2i$

$2i^{2}\sqrt{7}$

Change i squared to -1

$2(-1)\sqrt{7}$

$-2\sqrt{7}$

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Example Question #21 : Imaginary Numbers & Complex Functions

$\frac{\sqrt{-51}}{\sqrt{3}}$

Possible Answers:

$-\sqrt{17}$

$\sqrt{17}$

17i

$i\sqrt{17}$

$\sqrt{-17}$

Correct answer:

$i\sqrt{17}$

Explanation:

$\frac{\sqrt{-51}}{\sqrt{3}}$

Take i (the square root of -1) out of the radical.

$\frac{i\sqrt{51}}{\sqrt{3}}$

$i\sqrt{17}$

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Example Question #15 : Operations On Complex Numbers

$\sqrt{5}\cdot \sqrt{-42}$

Possible Answers:

$-2\sqrt{3}$

$i\sqrt{210}$

$5i\sqrt{14}$

$i\sqrt{47}$

Correct answer:

$i\sqrt{210}$

Explanation:

$\sqrt{5}\cdot \sqrt{-42}$

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

$\sqrt{5}\cdot i\sqrt{42}$

$i\sqrt{210}$

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Example Question #16 : Operations On Complex Numbers

$\sqrt{-45}\cdot \sqrt{72}$

Possible Answers:

$6i\sqrt{10}$

$-\sqrt{10}$

$i\sqrt{10}$

$4i\sqrt{10}$

$18i\sqrt{10}$

Correct answer:

$18i\sqrt{10}$

Explanation:

$\sqrt{-45}\cdot \sqrt{72}$

Take out i (the square root of -1) and then simplify before multiplying.

$i\sqrt{45}\cdot \sqrt{72}$

$i\sqrt{9\cdot 5}\cdot \sqrt{36\cdot 2}$

$3i\sqrt{5}\cdot 6\sqrt{2}$

$18i\sqrt{10}$

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Example Question #17 : Operations On Complex Numbers

$-\sqrt{-16}\cdot \sqrt{-40}$

Possible Answers:

$8\sqrt{5}$

$8\sqrt{10}$

$-4i\sqrt{10}$

$i\sqrt{10}$

$4\sqrt{5}$

Correct answer:

$8\sqrt{10}$

Explanation:

$-\sqrt{-16}\cdot \sqrt{-40}$

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.

$-i\sqrt{16}\cdot i\sqrt{40}$

$-4i\cdot i\sqrt{4\cdot 10}$

$-4i\cdot 2i\sqrt{10}$

$-8i^{2}\sqrt{10}$

$-8(-1)\sqrt{10}$

$8\sqrt{10}$

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Example Question #20 : Operations On Complex Numbers

$-\sqrt{-20}\cdot -\sqrt{32}$

Possible Answers:

$-8i\sqrt{10}$

$-4\sqrt{10}$

$8\sqrt{10}$

$8i\sqrt{10}$

$-8\sqrt{10}$

Correct answer:

$8i\sqrt{10}$

Explanation:

$-\sqrt{-20}\cdot -\sqrt{32}$

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

$-i\sqrt{20}\cdot -\sqrt{32}$

$-i\sqrt{5\cdot 4}\cdot -\sqrt{16\cdot 2}$

$-2i\sqrt{5}\cdot -4\sqrt{2}$

$8i\sqrt{10}$

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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 #11 : Operations On Complex Numbers

Example Question #12 : Operations On Complex Numbers

Example Question #21 : Imaginary Numbers & Complex Functions

Example Question #81 : Classifying Algebraic Functions

Example Question #91 : Algebra

Example Question #21 : Imaginary Numbers & Complex Functions

Example Question #15 : Operations On Complex Numbers

Example Question #16 : Operations On Complex Numbers

Example Question #17 : Operations On Complex Numbers

Example Question #20 : Operations On Complex Numbers

All GRE Subject Test: Math Resources

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