Roots of complex numbers (HSC SSCE Mathematics Extension 2): Flashcards
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What is the Fundamental Theorem of Algebra?
What is the Fundamental Theorem of Algebra?
Every non-zero polynomial has at least one complex root.
What is factorisation in polynomial equations?
What is factorisation in polynomial equations?
Expressing a polynomial as a product of simpler factors.
What does De Moivre's Theorem calculate?
What does De Moivre's Theorem calculate?
It calculates n-th roots of complex numbers using polar form.
What is the Argand Plane used for?
What is the Argand Plane used for?
Graphically representing complex numbers in 2D.
How do you find roots of z^2 + 1 = 0?
How do you find roots of z^2 + 1 = 0?
Solutions are z = i and z = -i using the quadratic formula.
What are the roots of z^3 - 1 = 0?
What are the roots of z^3 - 1 = 0?
Roots are z = 1, ω, ω² (cube roots of unity).
What is the formula for De Moivre's Theorem?
What is the formula for De Moivre's Theorem?
z^n = r^n (cos nθ + i sin nθ).
What is represented on the Argand Plane?
What is represented on the Argand Plane?
Complex numbers as points in a two-dimensional plane.
Why is factorisation essential for complex roots?
Why is factorisation essential for complex roots?
It helps break equations into solvable elements.
What is the significance of complex roots?
What is the significance of complex roots?
They provide a complete view of polynomial equations.