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Algebra 2
43. CC.HSN.CN.A.3
43.1 Complex conjugates
Complex Conjugates
Discover how to find the complex conjugate of a number, why multiplying by it always gives a real number, and how it locates polynomial roots.
What You'll Learn
Identify the complex conjugate of a plus bi as a minus bi by flipping the sign of the imaginary part
Calculate the product of a complex number and its conjugate to get a real number equal to a squared plus b squared
Apply complex conjugates to rationalize denominators containing imaginary numbers
Recognize that complex roots of a polynomial with real coefficients always occur in conjugate pairs
Use the complex conjugate root theorem to find a missing root once one complex root is known
Compare a complex number and its conjugate on the complex plane as reflections across the real axis
What You'll Practice
1
Finding conjugates of complex numbers with various formats
2
Adding a complex number to its conjugate
3
Rearranging non-standard complex number expressions
4
Combining operations with conjugates and addition of complex numbers
Why This Matters
Complex conjugates are essential for simplifying expressions and solving equations in advanced algebra and calculus. You'll use them to rationalize denominators, find polynomial roots, and work with complex-valued functions in engineering and physics applications.
Before You Start — Make Sure You Can:
This Unit Includes
4 Video lessons
Practice exercises
Learning resources
Skills
Complex Conjugates
Complex Numbers
Imaginary Numbers
Addition
Subtraction
Standard Form
Real and Imaginary Parts
IL Curriculum Aligned