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GRE Subject Test: Math : GRE Subject Test: Math

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

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Example Questions

Example Question #4 : Complex Conjugates

Simplify $\frac{14i+4}{7i-2}$

Possible Answers:

$\frac{20i-23}{24}$

$\frac{42i+99}{61}$

$\frac{3i-13}{9}$

$\frac{-91i+12}{15}$

$\frac{-90+56i}{-53}$

Correct answer:

$\frac{-90+56i}{-53}$

Explanation:

$\frac{14i+4}{7i-2}$

In problems like this, you are expected to simplify by removing i from the denominator. To do this, multiply the numerator and denominator by the conjugate of the denominator (switch the sign between the two terms from either a plus to a minus or vice versa) over itself. The conjugate over itself equals 1 and does not change the value of the expression (any number multiplied by 1 is still that number). Multiplying by the conjugate is the only way to eliminate i since there will be no middle term when we foil.

$\frac{14i+4}{7i-2}\cdot \frac{7i+2}{7i+2}$

$\frac{(14i+4)(7i+2)}{(7i-2)(7i+2)}$

$\frac{98i^{2}+28i+28i+8}{49i^{2}-4}$

Simplify i squared to -1 and then combine like terms

$\frac{98(-1)+28i+28i+8}{49(-1)-4}$

$\frac{-98+28i+28i+8}{-49-4}$

$\frac{-90+56i}{-53}$

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Example Question #3 : Complex Conjugates

Simplify $\frac{2+11i}{3-4i}$

Possible Answers:

$\frac{-38+41i}{25}$

$\frac{-9i-28}{11}$

$\frac{53i+8}{15}$

$\frac{30i+12}{15}$

$\frac{17+21i}{19}$

Correct answer:

$\frac{-38+41i}{25}$

Explanation:

$\frac{2+11i}{3-4i}$

$\frac{2+11i}{3-4i}\cdot \frac{3+4i}{3+4i}$

$\frac{(2+11i)(3+4i)}{(3-4i)(3+4i)}$

$\frac{6+33i+8i+44i^{2}}{9-16i^{2}}$

Simplify i squared to be -1 and then combine like terms

$\frac{6+33i+8i+44(-1)}{9-16(-1)}$

$\frac{6+33i+8i-44}{9+16}$

$\frac{-38+41i}{25}$

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Example Question #107 : Algebra

Simplify $\frac{7i}{-5+4i}$

Possible Answers:

$\frac{-11i-24}{9}$

$\frac{83i+46}{25}$

$\frac{-35i+28}{41}$

$\frac{42i-17}{45}$

$\frac{22i-14}{17}$

Correct answer:

$\frac{-35i+28}{41}$

Explanation:

$\frac{7i}{-5+4i}$

$\frac{7i}{-5+4i}\cdot \frac{-5-4i}{-5-4i}$

$\frac{7i(-5-4i)}{(-5+4i)(-5-4i)}$

$\frac{-35i-28i^{2}}{25-16i^{2}}$

Simplify i squared to be -1 and then combine like terms

$\frac{-35i-28(-1)}{25-16(-1)}$

$\frac{-35i+28}{25+16}$

$\frac{-35i+28}{41}$

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Example Question #4 : Complex Conjugates

Simplify $\frac{8i-2}{4i+6}$

Possible Answers:

$\frac{-16i-19}{13}$

$\frac{-63i+14}{12}$

$\frac{-20-56i}{-52}$

$\frac{32i+19}{34}$

$\frac{-5-14i}{-13}$

Correct answer:

$\frac{-5-14i}{-13}$

Explanation:

$\frac{8i-2}{4i+6}$

$\frac{8i-2}{4i+6}\cdot \frac{4i-6}{4i-6}$

$\frac{(8i-2)(4i-6)}{(4i+6)(4i-6)}$

$\frac{32i^{2}-8i-48i+12}{16i^{2}-36}$

Simplify i squared to be -1 and then combine like terms

$\frac{32(-1)-8i-48i+12}{16(-1)-36}$

$\frac{-32-8i-48i+12}{-16-36}$

$\frac{-20-56i}{-52}$

The coefficients of all the terms can divide by 4 so reduce each of them

$\frac{-5-14i}{-13}$

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Example Question #11 : Complex Conjugates

Simplify $\frac{2i}{9i+3}$

Possible Answers:

$\frac{23i-6}{72}$

$\frac{-18-6i}{-90}$

$\frac{-38+2i}{13}$

$\frac{49i+27}{52}$

$\frac{3+i}{15}$

Correct answer:

$\frac{3+i}{15}$

Explanation:

$\frac{2i}{9i+3}$

$\frac{2i}{9i+3}\cdot \frac{9i-3}{9i-3}$

$\frac{2i(9i-3)}{(9i+3)(9i-3)}$

$\frac{18i^{2}-6i}{81i^{2}-9}$

Simplify i squared to be -1 and then combine like terms

$\frac{18(-1)-6i}{81(-1)-9}$

$\frac{-18-6i}{-81-9}$

$\frac{-18-6i}{-90}$

Since each term divides by a greatest common factor of -6 reduce all of the coefficients. It would also be equivalent to divide by 6 to reduce all of the terms.

$\frac{3+i}{15}$

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Example Question #43 : Imaginary Numbers & Complex Functions

Simplify $\frac{-19i-8}{-5i-2}$

Possible Answers:

$\frac{47+78i}{21}$

$\frac{-30i+26}{13}$

$\frac{-111+2i}{-29}$

$\frac{10i-3}{29}$

$\frac{-78i+49}{5}$

Correct answer:

$\frac{-111+2i}{-29}$

Explanation:

$\frac{-19i-8}{-5i-2}$

$\frac{-19i-8}{-5i-2}\cdot \frac{-5i+2}{-5i+2}$

$\frac{(-19i-8)(-5i+2)}{(-5i-2)(-5i+2)}$

$\frac{95i^{2}+40i-38i-16}{25i^{2}-4}$

Simplify i squared to be -1 and then combine like terms

$\frac{95(-1)+40i-38i-16}{25(-1)-4}$

$\frac{-95+40i-38i-16}{-25-4}$

$\frac{-111+2i}{-29}$

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Example Question #111 : Classifying Algebraic Functions

Simplify $\frac{i-2}{3-i}$

Possible Answers:

$\frac{5-2i}{10}$

$\frac{7-i}{10}$

$\frac{i-7}{10}$

$\frac{2i-5}{5}$

$\frac{10i-2}{7}$

Correct answer:

$\frac{i-7}{10}$

Explanation:

$\frac{i-2}{3-i}$

$\frac{i-2}{3-i}\cdot \frac{3+i}{3+i}$

$\frac{(i-2)(3+i)}{(3-i)(3+i)}$

$\frac{3i+i^{2}-6-2i}{9-i^{2}}$

Simplify i squared to be -1 and combine like terms

$\frac{3i+(-1)-6-2i}{9-(-1)}$

$\frac{3i-1-6-2i}{9+1}$

$\frac{i-7}{10}$

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Example Question #112 : Classifying Algebraic Functions

Simplify $\frac{14i-9}{9+i}$

Possible Answers:

$\frac{23i-11}{65}$

$\frac{14i+111}{42}$

$\frac{135i-67}{82}$

$\frac{54i-18}{25}$

$\frac{-44i+63}{86}$

Correct answer:

$\frac{135i-67}{82}$

Explanation:

$\frac{14i-9}{9+i}$

$\frac{14i-9}{9+i}\cdot \frac{9-i}{9-i}$

$\frac{(14i-9)(9-i)}{(9+i)(9-i)}$

$\frac{126i-81-14i^{2}+9i}{81-i^{2}}$

Simplify i squared to be -1 and combine like terms

$\frac{126i-81-14(-1)+9i}{81-(-1)}$

$\frac{126i-81+14+9i}{81+1}$

$\frac{135i-67}{82}$

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Example Question #113 : Classifying Algebraic Functions

Simplify $\frac{13i+13}{13i-9}$

Possible Answers:

$\frac{26i-143}{125}$

$\frac{-13+169i}{250}$

$\frac{-13i-169}{-250}$

$\frac{26-143i}{250}$

$\frac{-26+143i}{-125}$

Correct answer:

$\frac{-26+143i}{-125}$

Explanation:

$\frac{13i+13}{13i-9}$

$\frac{13i+13}{13i-9}\cdot \frac{13i+9}{13i+9}$

$\frac{(13i+13)(13i+9)}{(13i-9)(13i+9)}$

$\frac{(169i^{2}+169i+117i+117)}{(169i^{2}-81)}$

Simplify i squared to be -1 and combine like terms

$\frac{(169(-1)+169i+117i+117)}{(169)(-1)-81}$

$\frac{(-169+169i+117i+117)}{(-169-81)}$

$\frac{-52+286i}{-250}$

Each term divides by 2 so make sure to reduce all of the terms

$\frac{-26+143i}{-125}$

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Example Question #114 : Classifying Algebraic Functions

Simplify $\frac{-12i-17}{6i+11}$

Possible Answers:

$\frac{24i-15}{81}$

$\frac{33i-105}{16}$

$\frac{-72i+13}{99}$

$\frac{19i+259}{-157}$

$\frac{-20i-187}{34}$

Correct answer:

$\frac{19i+259}{-157}$

Explanation:

$\frac{-12i-17}{6i+11}$

$\frac{-12i-17}{6i+11}\cdot \frac{6i-11}{6i-11}$

$\frac{(-12i-17)(6i-11)}{(6i+11)(6i-11)}$

$\frac{-72i^{2}+121i-102i+187}{36i^{2}-121}$

Simplify i squared to be -1 and combine like terms

$\frac{-72(-1)+121i-102i+187}{36(-1)-121}$

$\frac{72+121i-102i+187}{-36-121}$

$\frac{19i+259}{-157}$

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GRE Subject Test: Math : GRE Subject Test: Math

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #4 : Complex Conjugates

Example Question #3 : Complex Conjugates

Example Question #107 : Algebra

Example Question #4 : Complex Conjugates

Example Question #11 : Complex Conjugates

Example Question #43 : Imaginary Numbers & Complex Functions

Example Question #111 : Classifying Algebraic Functions

Example Question #112 : Classifying Algebraic Functions

Example Question #113 : Classifying Algebraic Functions

Example Question #114 : Classifying Algebraic Functions

All GRE Subject Test: Math Resources

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