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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #2 : Imaginary Numbers

Identify the real part of 1-3i

Possible Answers:

none of the above.

Correct answer:

Explanation:

A complex number in its standard form is of the form: a+bi , where stands for the real part and stands for the imaginary part. The symbol stands for $\sqrt{-1}$ .

The real part in this problem is 1.

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Example Question #11 : Sat Subject Test In Math I

Simplify:

(4-6i)+(7+2i)

Possible Answers:

3-4i

11-4i

-3+4i

5+2i

Correct answer:

11-4i

Explanation:

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

(4-6i)+(7+2i)=(4+7)+(-6+2)i=11-4i

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Example Question #2 : Complex Imaginary Numbers

Simplify:

(-5+5i)+(2-9i)

Possible Answers:

-3-4i

-3+4i

3-4i

-3i

Correct answer:

-3-4i

Explanation:

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

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

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Example Question #3 : Complex Imaginary Numbers

Simplify:

(-3+2i)+(5+8i)

Possible Answers:

2+10i

15-16i

10+2i

12i

Correct answer:

2+10i

Explanation:

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

(-3+2i)+(5+8i)=(-3+5)+(2+8)i=2+10i

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Example Question #2 : Imaginary Numbers

Simplify:

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

Possible Answers:

3+i

-4i

3+11i

-3-i

Correct answer:

-3-i

Explanation:

To subtract complex numbers, subtract the real terms together, then subtract the imaginary terms.

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

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Example Question #1 : Complex Imaginary Numbers

Simplify:

(12+8i)-(20+16i)

Possible Answers:

-8-8i

32+24i

-16i

8+8i

Correct answer:

-8-8i

Explanation:

To subtract complex numbers, subtract the real terms, then subtract the imaginary terms.

(12+8i)-(20+16i)=(12-20)+(8-16)i=-8-8i

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Example Question #1961 : Mathematical Relationships And Basic Graphs

Simplify:

(15-9i)-(6-10i)

Possible Answers:

9-i

9+i

21-19i

1+5i

Correct answer:

9+i

Explanation:

To subtract complex numbers, subtract the real terms, then subtract the imaginary terms.

(15-9i)-(6-10i)=(15-6)+(-9+10)i=9+i

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Example Question #2 : Imaginary Roots Of Negative Numbers

Simplify:

(5+8i)(6-2i)

Possible Answers:

16+32i

46+38i

25+8i

7+16i

Correct answer:

46+38i

Explanation:

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

(5+8i)(6-2i)=30-10i+48i-16i^2

Remember that $i=\sqrt-1$ , so i^2=-1 .

Substitute in for i^2

30-10i+48i-16i^2=30+38i-16(-1)=30+38i+16=46+38i

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Example Question #3 : Imaginary Roots Of Negative Numbers

Simplify:

(2+5i)(-8-i)

Possible Answers:

-18-5i

12+6i

42+11i

-11-42i

Correct answer:

-11-42i

Explanation:

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

(2+5i)(-8-i)=-16-2i-40i-5i^2

Remember that $i=\sqrt-1$ , so i^2=-1 .

Substitute in for i^2

-16-2i-40i-5i^2=-16-42i-5(-1)=-16+5-42i=-11-42i

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Example Question #4 : Imaginary Roots Of Negative Numbers

Simplify:

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

Possible Answers:

12-8i

-36-8i

-8+36i

36-8i

Correct answer:

-8+36i

Explanation:

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

(2+6i)(5+3i)=10+6i+30i+18i^2

Remember that $i=\sqrt-1$ , so i^2=-1 .

Substitute in for i^2

10+6i+30i+18i^2=10+36i+18(-1)=10-18+36i=-8+36i

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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2 : Imaginary Numbers

Example Question #11 : Sat Subject Test In Math I

Example Question #2 : Complex Imaginary Numbers

Example Question #3 : Complex Imaginary Numbers

Example Question #2 : Imaginary Numbers

Example Question #1 : Complex Imaginary Numbers

Example Question #1961 : Mathematical Relationships And Basic Graphs

Example Question #2 : Imaginary Roots Of Negative Numbers

Example Question #3 : Imaginary Roots Of Negative Numbers

Example Question #4 : Imaginary Roots Of Negative Numbers

All Algebra II Resources

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