Multiply Complex Numbers 2
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Question 1 of 5
1. Question
Solve
`(13-6i)^2`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.To solve `(13-6i)^2`, multiply and then simplify.`(13-6i)^2` Expand `(13-6i)^2`. `13^2+2times13times(-6i)+(-6i)^2` Take the square of `(-6i)^2` and `13^2`. `=` `169+2times13times(-6i)+36i^2` Multiply `2times13times(-6i)`. `=` `169-156i+36i^2` Replace `i^2=-1`. `=` `169-156i-36` Combine like terms `63` and `-1`. `=` `133-156i` `133-156i` -
Question 2 of 5
2. Question
Solve
`(3-4i)^2`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.To solve `(3-4i)^2`, multiply and then simplify.`(3-4i)^2` Expand `(3-4i)^2`. `(3-4i)(3-4i)` Multiply using the FOIL method. `=` `9 color(red)(-12i) color(red)(-12i)+16i^2` Combine like terms `-12i` and `-12i`. `=` `9 color(red)(-24i)+16i^2` Replace `i^2=-1`. `=` `9 -24i-16` Combine like terms `63` and `-1`. `=` `-7-24i` `-7-24i` -
Question 3 of 5
3. Question
Solve
`(6-6i)(7-6i)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.To solve `(6-6i)(7-6i)`, multiply and then simplify.`(6-6i)(7-6i)` Multiply using the FOIL method. `=` `42 color(red)(-36i) color(red)(-42i)+36i^2` Combine like terms `-36i` and `-42i`. `=` `42 color(red)(-78i)+36i^2` Replace `i^2=-1`. `=` `42-78i-36` Combine like terms `63` and `-1`. `=` `6-78i` `6-78i` -
Question 4 of 5
4. Question
Solve
`(-4-5i)^2`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.To solve `(-4-5i)^2`, multiply and then simplify.`(-4-5i)^2` Expand `(-4-5i)^2`. `(-4-5i)(-4-5i)` Multiply using the FOIL method. `=` `16+color(red)(20i)+color(red)(20i)+25i^2` Combine like terms `20i` and `20i`. `=` `16+color(red)(40i)+25i^2` Replace `i^2=-1`. `=` `16+40i-25` Combine like terms `16` and `-25`. `=` `-9+40i` `-9+40i` -
Question 5 of 5
5. Question
Solve
`(-2-3i)(-5+8i)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.To solve `(-2-3i)(-5+8i)`, multiply and then simplify.`(-2-3i)(-5+8i)` Multiply using the FOIL method. `=` `10 color(red)(-16i)+color(red)(15i)-24i^2` Combine like terms `-16i` and `15i`. `=` `10 color(red)(-i)-24i^2` Replace `i^2=-1`. `=` `10-i+24` Combine like terms `10` and `24`. `=` `34-i` `34-i`
Quizzes
- Simplify Roots of Negative Numbers 1
- Simplify Roots of Negative Numbers 2
- Powers of the Imaginary Unit 1
- Powers of the Imaginary Unit 2
- Solve Quadratic Equations with Complex Solutions 1
- Solve Quadratic Equations with Complex Solutions 2
- Equality of Complex Numbers
- Add and Subtract Complex Numbers 1
- Add and Subtract Complex Numbers 2
- Multiply Complex Numbers 1
- Multiply Complex Numbers 2
- Divide Complex Numbers
- Complex Numbers – Product of Linear Factors 1
- Complex Numbers – Product of Linear Factors 2
- Mixed Operations with Complex Numbers