Complex Numbers and the Fundamental Theorem of Algebra
Aligned to N-CN.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
The imaginary unit i is defined as the square root of negative one, which lets us solve equations that have no real solutions. A complex number has a real part and an imaginary part, and the Fundamental Theorem of Algebra says every polynomial has a full set of roots among the complex numbers.
Worked example
Simplify the square root of -9. Write it as the square root of 9 times the square root of -1, which is 3i.
Practice questions
- What does i equal?
- Simplify the square root of -16.
- Add the complex numbers (2 + 3i) and (1 + 4i).
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Números complejos y el Teorema Fundamental del Álgebra
La unidad imaginaria i se define como la raíz cuadrada de menos uno, lo que nos permite resolver ecuaciones que no tienen soluciones reales. Un número complejo tiene una parte real y una parte imaginaria, y el Teorema Fundamental del Álgebra establece que todo polinomio tiene un conjunto completo de raíces entre los números complejos.
Ejemplo: Simplifica la raíz cuadrada de -9. Escríbela como la raíz cuadrada de 9 por la raíz cuadrada de -1, lo que es igual a 3i.
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