Complex Numbers and Polynomials
Students will use complex numbers to find roots of polynomial equations, especially those with real coefficients.
Key Questions
- Explain the Conjugate Root Theorem for polynomials with real coefficients.
- Analyze how complex roots appear in conjugate pairs for real polynomials.
- Construct the remaining roots of a polynomial given one complex root.
MOE Syllabus Outcomes
Suggested Methodologies
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More in Complex Systems: Complex Numbers
Introduction to Complex Numbers
Students will define imaginary numbers, complex numbers, and perform basic arithmetic operations.
2 methodologies
Complex Conjugates and Division
Students will understand complex conjugates and use them to perform division of complex numbers.
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Argand Diagram and Modulus-Argument Form
Students will represent complex numbers geometrically on an Argand diagram and convert to modulus-argument form.
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Multiplication and Division in Polar Form
Students will perform multiplication and division of complex numbers using their modulus-argument forms.
2 methodologies
De Moivre's Theorem
Students will apply De Moivre's Theorem to find powers and roots of complex numbers.
2 methodologies