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 `1i`.`(6)/(1+i)` Multiply the numerator and the denominator by the conjugate `1i`. `=` `(6)/(1+i)timescolor(red)(1i)/color(red)(1i)` `=` `(66i)/(1i+ii^2)` Combine like terms `i` and `i`. `=` `(66i)/(1i^2)` Remember that `i^2=1`. `=` `(66i)/(1(1))` Simplify `=` `(66i)/(2)` Divide both terms in the numerator by `2`. `=` `33i` `33i` 
Question 2 of 6
2. Question
Solve
`(73i)/(4i)`
Correct
Great Work!
Incorrect
Imaginary numbers has the property `i^2=1`.To solve `(73i)/(4i)`, multiply the numerator and the denominator by `i` and then simplify.`(73i)/(4i)` Multiply the numerator and the denominator by `i`. `=` `(73i)/(4i)timescolor(red)(i)/color(red)(i)` `=` `(7i3i^2)/(4i^2)` Remember that `i^2=1`. `=` `(7i3(1))/(4(1))` Simplify `=` `(7i+3)/(4)` Divide both terms in the numerator by `4`. `=` `7/4i3/4` 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)/(13i)`
Correct
Great Work!
Incorrect
Imaginary numbers has the property `i^2=1`.To solve `(i)/(13i)`, multiply the numerator and the denominator by the conjugate of the denominator and then simplify. The conjugate of `(i)/(13i)` is `1+3i`.`(i)/(13i)` Multiply the numerator and the denominator by the conjugate `1+3i`. `=` `(i)/(13i)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`. `=` `(i3)/(1 + 9)` Simplify `=` `i/103/10` Divide both terms in the numerator by `10`. `=` `(3)/10 + i/10` Rearrange. `(3)/10 + i/10` 
Question 4 of 6
4. Question
Solve
`(72i)/(5i)`
Correct
Great Work!
Incorrect
Imaginary numbers has the property `i^2=1`.To solve `(72i)/(5i)`, multiply the numerator and the denominator by the conjugate of the denominator and then simplify. The conjugate of `(72i)/(5i)` is `i`.`(72i)/(5i)` Multiply the numerator and the denominator by the conjugate `i`. `=` `(72i)/(5i)timescolor(red)(i)/color(red)(i)` `=` `(7i2i^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
`(59i)/(1+i)`
Correct
Great Work!
Incorrect
Imaginary numbers has the property `i^2=1`.To solve `(59i)/(1+i)`, multiply the numerator and the denominator by the conjugate of the denominator and then simplify. The conjugate of `(59i)/(1+i)` is `1i`.`(59i)/(1+i)` Multiply the numerator and the denominator by the conjugate `1i`. `=` `(55i9i+9i^2)/(1^2i^2)` Remember that `i^2=1`. `=` `(55i9i9)/(1+1)` Combine the terms with `i`. `=` `(514i9)/(1+1)` Combine the real numbers. `=` `(414i)/(2)` Divide both terms in the numerator by `2`. `=` `(4)/2(14i)/(2)` Simplify. `=` `27i` `27i` 
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 `32i`.`(2+3i)/(3+2i)` Multiply the numerator and the denominator by the conjugate `32i`. `=` `(2+3i)/(3+2i)timescolor(red)(32i)/color(red)(32i) `=` `(64i+9i6i^2)/(3^2(2i)^2)` Take the square of `(2i)^2` and `3^2`. `=` `(64i+9i6i^2)/(94i^2)` Remember that `i^2=1`. `=` `(64i+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