Argand diagrams Flashcards
Which axis on an Argand diagram is imaginary, and which is real?
The y axis is Im, and the x axis is Re.
What is the modulus of a point?
The distance from the origin to that point. Square both parts, sum, and then square root.
What is the argument of a point?
The angle created by its line to the origin, and the positive real axis.
How do you work out the argument?
for complex number z = x + iy
If in the top right (first quadrant), then arg z = arctan(y/x)
If in the second (top left), then arg z = pi - arctan(y/x)
If in the third (bottom left), then arg z = -(pi - arctan(y/x))
If in the fourth (bottom right), then arg z = -arctan(y/x)
What is the modulus argument form of a complex number with modulus r and argument theta?
z = r(costheta + isintheta)
For complex numbers z1 and z2, what is the modulus of the product?
The individual moduli, multiplied together.
For complex numbers z1 and z2, what is the arg(z1 x z2)?
arg z1 + arg z2
What is the arg (z1/z2)?
arg z1 - arg z2
How do you represent the distance between z1 and z2?
Modulus( z2 - z1)
What describes the circle with centre (x1,y1) and radius r?
Modulus( z - z1) = r
What represents the perpendicular bisector of the line joining z1 and z2?
Modulus (z - z1) = Modulus (z - z2)
What is a half line?
A straight line extending infinitely from a point in one direction.
How is a half line from z1 represented, making an angle theta between the half line, and a line from the point parallel to the real axis?
arg (z - z1) = theta
Modulus (z - 4 -2i) would represent what complex number?
4 + 2i
