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College Algebra : Complex Numbers

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Example Questions

Example Question #21 : Complex Numbers

Simplify:

-6+12i+(-2-3i)

Possible Answers:

4-6i

4+5i

-8+9i

8+9i

Correct answer:

-8+9i

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

-6+12i+(-2-3i)=-6+12i-2-3i

Combine like terms- combine the real numbers together and the imaginary numbers together:

-6+12i-2-3i=(-6-2)+(12i-3i)

(-6-2)+(12i-3i)=-8+9i

This gives a final answer of -8+9i

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Example Question #132 : Review And Other Topics

Simplify:

5-2i+(4-3i)

Possible Answers:

9-6i

1-5i

10+5i

9-5i

Correct answer:

9-5i

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

5-2i+(4-3i)=5-2i+4-3i

Combine like terms- combine the real numbers together and the imaginary numbers together:

5-2i+4-3i=(5+4)+(-2i-3i)

(5+4)+(-2i-3i)=9-5i

This gives a final answer of 9-5i

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Example Question #23 : Complex Numbers

Simplify:

11+3i+(-2+6i)

Possible Answers:

-9+9i

1+i

9+9i

9-i

Correct answer:

9+9i

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

11+3i+(-2+6i)=11+3i-2+6i

Combine like terms- combine the real numbers together and the imaginary numbers together:

11+3i-2+6i=(11-2)+(3i+6i)

(11-2)+(3i+6i)=9+9i

This gives a final answer of 9+9i

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Example Question #24 : Complex Numbers

Simplify:

6-5i-(-12-4i)

Possible Answers:

18-i

9-i

18+9i

-6-i

Correct answer:

18-i

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

6-5i-(-12-4i)=6-5i+12+4i

Combine like terms- combine the real numbers together and the imaginary numbers together:

6-5i+12+4i=(6+12)+(-5i+4i)

(6+12)+(-5i+4i)=18-i

This gives a final answer of 18-i

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Example Question #22 : Complex Numbers

Simplify:

16-3i-(12-2i)

Possible Answers:

4-5i

4-i

28-i

4+5i

Correct answer:

4-i

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

16-3i-(12-2i)=16-3i-12+2i

Combine like terms- combine the real numbers together and the imaginary numbers together:

16-3i-12+2i=(16-12)+(-3i+2i)

(16-12)+(-3i+2i)=4-i

This gives a final answer of 4-i

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Example Question #417 : College Algebra

Rewrite in standard form:

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

Possible Answers:

$\frac{2}{7}+\frac{7i}{12}$

None of these

$\frac{2}{17}+\frac{12i}{17}$

$\frac{2}{7}+\frac{12i}{7}$

$\frac{1}{7}+\frac{i}{7}$

Correct answer:

$\frac{2}{17}+\frac{12i}{17}$

Explanation:

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

Multiply ply by the conjugate:

$\frac{3+3i}{5-3i}\times \frac{5+3i}{5+3i}=\frac{15+9i+15i+9i^2}{25-9i^2}$

Simplify:

$\frac{15+9i+15i+9i^2}{25-9i^2}=\frac{6+24i}{34}\rightarrow \boldsymbol{\frac{6}{34}+\frac{12i}{17}}$

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Example Question #418 : College Algebra

Rewrite in standard form:

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

Possible Answers:

$\frac{-1}{2}-\frac{5}{2}i$

$\frac{-1}{2}+\frac{5}{2}i$

$\frac{1}{2}+\frac{5}{2}i$

$\frac{1}{2}-\frac{5}{2}i$

None of these

Correct answer:

$\frac{-1}{2}-\frac{5}{2}i$

Explanation:

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

Find a common denominator and subtract.

To do so multiply the numerator and denominator of both fractions by the denominator of the opposite fraction:

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

Combine and simplify:

$\frac{2-2i-3-3i}{1-i^2}\rightarrow \frac{-1-5i}{2}\rightarrow \boldsymbol{\frac{-1}{2}-\frac{5}{2}i}$

Keep in mind

i^2=-1

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College Algebra : Complex Numbers

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #21 : Complex Numbers

Example Question #132 : Review And Other Topics

Example Question #23 : Complex Numbers

Example Question #24 : Complex Numbers

Example Question #22 : Complex Numbers

Example Question #417 : College Algebra

Example Question #418 : College Algebra

All College Algebra Resources

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