Properties of moduli and arguments (HSC SSCE Mathematics Extension 2): Flashcards
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What does modulus represent in complex numbers?
What does modulus represent in complex numbers?
It represents the magnitude of the complex number.
How is the modulus of a complex number defined?
How is the modulus of a complex number defined?
|z| = √(x² + y²) for z = x + iy.
What does the argument of a complex number denote?
What does the argument of a complex number denote?
It denotes the direction of the complex number.
What is the principal argument range?
What is the principal argument range?
-π < θ ≤ π.
How can complex numbers be expressed in polar form?
How can complex numbers be expressed in polar form?
As r cis θ, where cis θ = cos θ + i sin θ.
What is the product of moduli property?
What is the product of moduli property?
|z1 z2| = |z1| |z2|.
What is the property of the sum of arguments in complex numbers?
What is the property of the sum of arguments in complex numbers?
arg(z1 z2) = arg(z1) + arg(z2) + 2kπ, k ∈ Z.
How is the conjugate of a complex number expressed?
How is the conjugate of a complex number expressed?
Conjugate: z̄ = r cis (-θ).
What does De Moivre's Theorem state?
What does De Moivre's Theorem state?
z^n = r^n cis(nθ) for powers of complex numbers.
What is the purpose of Argand diagrams?
What is the purpose of Argand diagrams?
They visually represent complex numbers geometrically.