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High School Math : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Using Expressions With Complex Numbers

Solve the following complex number equation:

$2n^2=\frac{-27}{8}$

Possible Answers:

$n=\frac{3i\sqrt{3}}{4}, \frac{-3i\sqrt{3}}{4}$

$n=\frac{3i\sqrt{3}}{2}$

$n=\frac{3i\sqrt{3}}{4}$

$n=\frac{3i\sqrt{3}}{2}, \frac{-3i\sqrt{3}}{2}$

$n=\frac{-3i\sqrt{3}}{4}$

Correct answer:

$n=\frac{3i\sqrt{3}}{4}, \frac{-3i\sqrt{3}}{4}$

Explanation:

Begin by simplifying the equation. Divide both sides by and take the square root.

$2n^2=\frac{-27}{8}$

$n^2=\frac{-27}{16}$

$n=\frac{\sqrt{-27}}{\sqrt{16}}$

$n=\frac{3i\sqrt{3}}{4}, \frac{-3i\sqrt{3}}{4}$

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Example Question #5 : Using Expressions With Complex Numbers

Solve the following complex number equation:

4x^2+75=0

Possible Answers:

$x=\frac{5i\sqrt{3}}{2}, -\frac{5i\sqrt{3}}{2}$

$x= -\frac{5i\sqrt{3}}{2}$

$x=\frac{5i\sqrt{3}}{3}, -\frac{5i\sqrt{3}}{3}$

$x=\frac{5i\sqrt{3}}{2}$

$x=\frac{5i\sqrt{3}}{3}$

Correct answer:

$x=\frac{5i\sqrt{3}}{2}, -\frac{5i\sqrt{3}}{2}$

Explanation:

Begin by simplifying the equation. Divide both sides by and take the square root.

4x^2+75=0

4x^2=-75

$x^2=\frac{-75}{4}$

$x=\frac{\sqrt{-75}}{\sqrt{4}}$

$x=\frac{5i\sqrt{3}}{2}, -\frac{5i\sqrt{3}}{2}$

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Example Question #3 : Using Expressions With Complex Numbers

Solvethe following complex number expression for :

2n^2+18=0

Possible Answers:

n=4i, -4i

n=3i, -3i

n=2i, -2i

n=6i, -6i

n=5i, -5i

Correct answer:

n=3i, -3i

Explanation:

Solve the equation using complex numbers:

2n^2+18=0

2n^2=-18

n^2=-9

$n=\sqrt{-9}$

n=3i, -3i

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Example Question #11 : Using Expressions With Complex Numbers

Simplify the following complex number expression:

$(\sqrt{-6})(\sqrt{-4})(\sqrt{-3})$

Possible Answers:

$-6i\sqrt{2}$

$-4i\sqrt{3}$

$-6i\sqrt{3}$

$-6i\sqrt{5}$

$-4i\sqrt{2}$

Correct answer:

$-6i\sqrt{2}$

Explanation:

Begin by simplifying the radicals using complex numbers:

$(\sqrt{-6})(\sqrt{-4})(\sqrt{-3})$

$=(i\sqrt{6})(2i)(i\sqrt{3})$

Multiply the factors:

$=(2i^2\sqrt{6})(i\sqrt{3})$

$=(2i^3\sqrt{18})$

Simplify. Remember that i^3 is equivalent to .

$=-2i\sqrt{18}$

$=-6i\sqrt{2}$

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Example Question #41 : Algebra Ii

Simplify the following complex number expression:

(3i^3)(2i)^2

Possible Answers:

12i

10i

11i

Correct answer:

12i

Explanation:

Begin by completing the square:

(3i^3)(2i)^2

=(3i^3)(4i^2)

Multiply the factors:

=(12i^5)

Simplify. Remember that i^5 is equivalent to .

=12i

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Example Question #12 : Using Expressions With Complex Numbers

Simplify the following complex number expression:

(-2i)^4(-4i^3)

Possible Answers:

80i

36i

72i

12i

64i

Correct answer:

64i

Explanation:

Begin by completing the square:

(-2i)^4(-4i^3)

=(16i^4)(-4i^3)

Now, multiply the factors:

=(16i^4)(-4i^3)

=(-64i^7)

Simplify. Remember that i^7 is equivalent to .

=64i

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Example Question #13 : Using Expressions With Complex Numbers

Simplify the following complex number expression:

(7+2i)(5-3i)

Possible Answers:

42-12i

44-14i

43-13i

40-10i

41-11i

Correct answer:

41-11i

Explanation:

Use the FOIL (First, Outer, Inner, Last) to multiply the complex numbers:

(7+2i)(5-3i)

=35-21i+10i-6i^2

Combine like terms and simplify. Remember that i^2 is equivalent to .

=35-11i-6i^2

=35-11i+6

=41-11i

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Example Question #41 : Algebra Ii

Simplify the following complex number expression:

$\frac{4+3i}{1-2i}$

Possible Answers:

$\frac{-4+11i}{5}$

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

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

$\frac{-2+11i}{5}$

$\frac{-3+11i}{5}$

Correct answer:

$\frac{-2+11i}{5}$

Explanation:

Begin by multiplying the numerator and denominator by the conjugate of the denominator:

$=\frac{4+3i}{1-2i}$ $\cdot \frac{1+2i}{1+2i}$

$=\frac{4+8i+3i+6i^2}{1-4i^2}$

Combine like terms:

$=\frac{4+11i+6i^2}{1-4i^2}$

Simplify. Remember that i^2 is equivalent to .

$=\frac{4+11i-6}{1+4}$

$=\frac{-2+11i}{5}$

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Example Question #12 : Using Expressions With Complex Numbers

Simplify the following complex number expression:

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

Possible Answers:

-i^2

i^3

i^2

Correct answer:

Explanation:

Begin by multiplying the numerator and denominator by the conjugate of the denominator:

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

$=\frac{4-4i-4i+4i^2}{4-4i^2}$

Combine like terms:

$=\frac{4-8i+4i^2}{4-4i^2}$

Simplify. Remember that i^2 is equivalent to .

$=\frac{4-8i-4}{4+4}$

$=\frac{-8i}{8}$

=-i

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Example Question #12 : Using Expressions With Complex Numbers

Simplify the following expression:

(5 + 3i) + (2 - 6i)

Possible Answers:

3 - 3i

7 + 9i

7 + 3i

7 - 3i

7 - 9i

Correct answer:

7 - 3i

Explanation:

Simplifying expressions with complex numbers uses exactly the same process as simplifying expressings with one variable. In this case, behaves similarly to any other variable. Thus, we have:

(5 + 3i) + (2 - 6i) = (5 +2) + (3 - 6)i = 7 - 3i

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High School Math : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : Using Expressions With Complex Numbers

Example Question #5 : Using Expressions With Complex Numbers

Example Question #3 : Using Expressions With Complex Numbers

Example Question #11 : Using Expressions With Complex Numbers

Example Question #41 : Algebra Ii

Example Question #12 : Using Expressions With Complex Numbers

Example Question #13 : Using Expressions With Complex Numbers

Example Question #41 : Algebra Ii

Example Question #12 : Using Expressions With Complex Numbers

Example Question #12 : Using Expressions With Complex Numbers

All High School Math Resources

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