Topic 2: Argand Diagrams Flashcards
What is represented by the y-axis in argand diagrams?
Imaginary numbers
What is represented by the x-axis in argand diagrams?
Real numbers
What 2 things can complex numbers be?
Cartesian coordinates or vectors.
What is the modulus of a complex number,|z|?
The modulus,|z|, is the distance from the origin to a point on an Argand diagram. It can be calculated by √(x2 + y2).
What is the argument of a complex number, arg(z)?
The argument, arg(z), is the angle between the positive real axis and the line joining that number to the origin. It satisfies tanθ=y/x.
What are radians?
The angle made if you were to take the radius of a circle and stretched it around the circumference. e.g. A full circle is 2π radians. 1 radian≈57.296°.
How is modulus-argument form for a complex number (z) written?
z=r(cosθ+𝐢sinθ), r being the|z|and θ being argz.
What does |z₁z₂| equal?
|z₁||z₂|
What does arg(z₁z₂) equal?
arg(z₁)+arg(z₂)
What does |z₁z₂| equal?
|z₁|/| z₂|
What does arg(z₁/z₂) equal?
arg(z₁) - arg(z₂)
What is |z₁ - z₂|?
The distance between z₁ and z₂
What does |z - z₁|= r mean?
A circle with coordinates z₁ and a radius of r.
What does |z - z₁|=|z - z₂| mean?
The perpendicular bisector of the line connecting z₁ and z₂.
What is arg(z - z₁)?
A half-line: a straight line extending from a point infinitely in only one direction.
