Rationalize the Denominator with Imaginary and Complex Numbers

Learn how to rationalize the denominator when you have a complex or imaginary number below the fraction bar! Mario's Math Tutoring breaks down two key cases: when you have a single imaginary term (monomial) and when you have a complex binomial. Master the use of the complex conjugate to eliminate 'i' from the denominator and write your final answer in standard a + bi form. In this video, you'll discover: 0:00 Introduction to Rationalizing Complex Denominators 0:30 Why We Rationalize (Getting Rid of 'i' in the Denominator) 0:50 Case 1: Monomial Denominator (Multiplying by i/i) 1:30 Remember: i² = -1 1:50 Example 1: Rationalizing 3 / 2i 2:30 Case 2: Binomial Denominator (Multiplying by the Complex Conjugate) 3:00 What is a Complex Conjugate? 3:40 Example 2: Rationalizing 5 / (2 - i) 4:50 Important: Writing the Final Answer in a + bi Form 5:20 Example 3: Rationalizing (-4 - i) / (3 + 2i) 6:00 Common Mistake: Changing All Signs in the Conjugate 7:40 Example 4: Rationalizing (7 + 5i) / (1 - i) 8:30 Shortcut for Denominator When Using Conjugate 9:50 Example 5: Rationalizing 4 / (7 + 5i) 10:30 Algebra 1 & Algebra 2 Video Courses Mention Master rationalizing complex denominators and confidently work with complex fractions! #ComplexNumbers #RationalizeDenominator #ImaginaryNumbers #ComplexConjugate #Algebra2 #Precalculus #MathTutorial #MathHelp ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join