Divide Complex Numbers
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Question 1 of 6
1. Question
Solve
`(6)/(1+i)`
Correct
Great Work!
Incorrect
Imaginary numbers has the property `i^2=-1`.To solve `(6)/(1+i)`, multiply the numerator and the denominator by the conjugate of the denominator and then simplify. The conjugate of `(6)/(1+i)` is `1-i`.`(6)/(1+i)` Multiply the numerator and the denominator by the conjugate `1-i`. `=` `(6)/(1+i)timescolor(red)(1-i)/color(red)(1-i)` `=` `(6-6i)/(1-i+i-i^2)` Combine like terms `-i` and `i`. `=` `(6-6i)/(1-i^2)` Remember that `i^2=-1`. `=` `(6-6i)/(1-(-1))` Simplify `=` `(6-6i)/(2)` Divide both terms in the numerator by `2`. `=` `3-3i` `3-3i` -
Question 2 of 6
2. Question
Solve
`(-7-3i)/(4i)`
Correct
Great Work!
Incorrect
Imaginary numbers has the property `i^2=-1`.To solve `(-7-3i)/(4i)`, multiply the numerator and the denominator by `i` and then simplify.`(-7-3i)/(4i)` Multiply the numerator and the denominator by `i`. `=` `(-7-3i)/(4i)timescolor(red)(i)/color(red)(i)` `=` `(-7i-3i^2)/(4i^2)` Remember that `i^2=-1`. `=` `(-7i-3(-1))/(4(-1))` Simplify `=` `(-7i+3)/(-4)` Divide both terms in the numerator by `-4`. `=` `7/4i-3/4` Reverse the order of the terms. The term with the `i` should be the second term. `=` `-3/4+7/4i` `-3/4+7/4i` -
Question 3 of 6
3. Question
Solve
`(i)/(1-3i)`
Correct
Great Work!
Incorrect
Imaginary numbers has the property `i^2=-1`.To solve `(i)/(1-3i)`, multiply the numerator and the denominator by the conjugate of the denominator and then simplify. The conjugate of `(i)/(1-3i)` is `1+3i`.`(i)/(1-3i)` Multiply the numerator and the denominator by the conjugate `1+3i`. `=` `(i)/(1-3i)timescolor(red)(1+3i)/color(red)(1+3i)` `=` `(i+3i^2)/(1^2 – (3i)^2)` Take the square of `(3i)^2`. `=` `(i+3i^2)/(1 – 9i^2)` Remember that `i^2=-1`. `=` `(i-3)/(1 + 9)` Simplify `=` `i/10-3/10` Divide both terms in the numerator by `10`. `=` `(-3)/10 + i/10` Rearrange. `(-3)/10 + i/10` -
Question 4 of 6
4. Question
Solve
`(-7-2i)/(5i)`
Correct
Great Work!
Incorrect
Imaginary numbers has the property `i^2=-1`.To solve `(-7-2i)/(5i)`, multiply the numerator and the denominator by the conjugate of the denominator and then simplify. The conjugate of `(-7-2i)/(5i)` is `i`.`(-7-2i)/(5i)` Multiply the numerator and the denominator by the conjugate `i`. `=` `(-7-2i)/(5i)timescolor(red)(i)/color(red)(i)` `=` `(-7i-2i^2)/(5i^2)` Remember that `i^2=-1`. `=` `(-7i+2)/(-5)` Divide both terms in the numerator by `-5`. `=` `(-7i)/(-5) + 2/(-5)` Rearrange. `=` `2/(-5) – (7i)/(-5)` Simplify. `=` `(-2)/5 + (7i)/5` `(-2)/5 + (7i)/5` -
Question 5 of 6
5. Question
Solve
`(5-9i)/(1+i)`
Correct
Great Work!
Incorrect
Imaginary numbers has the property `i^2=-1`.To solve `(5-9i)/(1+i)`, multiply the numerator and the denominator by the conjugate of the denominator and then simplify. The conjugate of `(5-9i)/(1+i)` is `1-i`.`(5-9i)/(1+i)` Multiply the numerator and the denominator by the conjugate `1-i`. `=` `(5-5i-9i+9i^2)/(1^2-i^2)` Remember that `i^2=-1`. `=` `(5-5i-9i-9)/(1+1)` Combine the terms with `i`. `=` `(5-14i-9)/(1+1)` Combine the real numbers. `=` `(-4-14i)/(2)` Divide both terms in the numerator by `2`. `=` `(-4)/2-(14i)/(2)` Simplify. `=` `-2-7i` `-2-7i` -
Question 6 of 6
6. Question
Solve
`(2+3i)/(3+2i)`
Correct
Great Work!
Incorrect
Imaginary numbers has the property `i^2=-1`.To solve `(2+3i)/(3+2i)`, multiply the numerator and the denominator by the conjugate of the denominator and then simplify. The conjugate of `(2+3i)/(3+2i)` is `3-2i`.`(2+3i)/(3+2i)` Multiply the numerator and the denominator by the conjugate `3-2i`. `=` `(2+3i)/(3+2i)timescolor(red)(3-2i)/color(red)(3-2i) `=` `(6-4i+9i-6i^2)/(3^2-(2i)^2)` Take the square of `(2i)^2` and `3^2`. `=` `(6-4i+9i-6i^2)/(9-4i^2)` Remember that `i^2=-1`. `=` `(6-4i+9i+6)/(9 + 4)` Combine the terms with `i`. `=` `(6+5i+6)/(9 + 4)` Combine all real numbers. `=` `(12+5i)/13` Divide both terms in the numerator by `13`. `=` `12/13+(5i)/13` `12/13+(5i)/13`
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