Dividing
Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 25 of 51.
A fraction with i in the bottom is not finished: the form a + bi needs a real number underneath. To get one, multiply top and bottom by the conjugate of the bottom. That is allowed because you are multiplying by a fraction equal to 1.
Take (5 + 5i)/(2 + i). The conjugate of the bottom is 2 - i. The bottom becomes (2 + i)(2 - i), which is 4 + 1, so 5. The top becomes (5 + 5i)(2 - i) = 10 - 5i + 10i - 5i^2, which is 15 + 5i. Then split the fraction: (15 + 5i)/5 = 3 + i.
Check by multiplying back: (2 + i)(3 + i) is 6 + 5i + i^2, which is 5 + 5i.
Challenge
Divide (7 + i)/(1 + i) and write the answer as a + bi.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Quadratics & Complex Numbers
2Completing the Square
Perfect Square TrinomialsThe Missing NumberCompleting the SquareIrrational AnswersWhen a Is Not 1Recap: Completing the Square5Complex Arithmetic
Adding and SubtractingMultiplyingThe ConjugateDividingA Pure Imaginary BottomRecap: Complex Arithmetic8Lines Meet Parabolas
Two CrossingsJust TouchingNo MeetingA Circle and a LineRecap: Lines and Parabolas