Curves and regions on the complex plane (HSC SSCE Mathematics Extension 2): Flashcards
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10 cards from this deck
What is a complex number?
What is a complex number?
A number in the form a + bi, where i^2 = -1.
What does the Argand diagram represent?
What does the Argand diagram represent?
It shows complex numbers as points (x, y) on a plane.
What is the complex conjugate of z = a + bi?
What is the complex conjugate of z = a + bi?
The conjugate is a - bi, reversing the imaginary part.
What is the modulus of a complex number?
What is the modulus of a complex number?
It's the distance from the origin, |z| = √(x² + y²).
How is multiplication by i visualized?
How is multiplication by i visualized?
It results in a 90° anticlockwise rotation around the origin.
What does arg(z) = π/3 indicate?
What does arg(z) = π/3 indicate?
It indicates a line with a fixed angle on the complex plane.
What is the modulus-argument form of z?
What is the modulus-argument form of z?
z = r(cos θ + i sin θ), where r is the modulus.
How do you visualize addition of complex numbers?
How do you visualize addition of complex numbers?
Use vector addition and the parallelogram rule.
What does the reflection of a conjugate show?
What does the reflection of a conjugate show?
It shows symmetry across the real axis.
What do inequalities define on the complex plane?
What do inequalities define on the complex plane?
They create distinguishable regions or areas.