Modulus and argument (HSC SSCE Mathematics Extension 2): Flashcards
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What is the formula for the modulus of a complex number?
What is the formula for the modulus of a complex number?
|z| = √(x² + y²) where z = x + iy.
What does the argument of a complex number represent?
What does the argument of a complex number represent?
It indicates the direction of z on the Argand diagram.
What is the range for the principal value of argument?
What is the range for the principal value of argument?
-π < θ ≤ π.
How is the polar form of a complex number expressed?
How is the polar form of a complex number expressed?
z = r(cos θ + i sin θ) = r · cis θ.
How do you find the modulus of z = 3 + 4i?
How do you find the modulus of z = 3 + 4i?
|z| = √(3² + 4²) = 5.
What is the argument of z = 3 + 4i?
What is the argument of z = 3 + 4i?
θ = tan⁻¹(4/3) ≈ 0.93 radians.
What is the modulus of the product of two complex numbers?
What is the modulus of the product of two complex numbers?
|z₁z₂| = |z₁||z₂|.
How is the argument of a product of complex numbers calculated?
How is the argument of a product of complex numbers calculated?
arg(z₁z₂) = arg(z₁) + arg(z₂).
What is the modulus of the quotient of two complex numbers?
What is the modulus of the quotient of two complex numbers?
|z₁/z₂| = |z₁|/|z₂|.
How do you find the argument of a quotient of complex numbers?
How do you find the argument of a quotient of complex numbers?
arg(z₁/z₂) = arg(z₁) - arg(z₂).