Chapter 8 Loci In The Argand Diagram

Question 1

What does |z - a|=|z - b| represent?

Answer 1

This represents the perpendicular bisector of the points a and b

Question 2

What does arg(z - a) = θ represent?

Answer 2

arg(z - a)=θ represents a half line starting at z = a at an angle θ from the positive real direction

Question 3

What does |z - a| < r represent?

Answer 3

|z - a| < r represents the interior of the circle.

Question 4

What does |z - a| > r represent?

Answer 4

|z - a| > r represents the exterior of the circle.

Question 5

What does |z - a| = r represent?

Answer 5

|z - a |= r represents a circle, centered at a with radius r.

Question 6

What is the distance between points z and z’ in an Argand diagram?

Answer 6

The distance is |z - z’|

Question 7

What is the modulus-argument form of z?

Answer 7

The modulus-argument form of z is
z= r(cos(θ) + i sin(θ)), where r = |z| and θ=arg(z)

Question 8

What is the relationship between two complex numbers w and z?

Answer 8

Question 9

What is the modulus of
z = x + yi?

Answer 9

The modulus of z = x + yi is |z| = √(x² + y²).

Question 10

What is the argument of z?

Answer 10

The argument of z is the angle θ, measured in radians, between the line connecting the origin and the point z and the positive real axis.

Question 11

What is the principal argument of z?

Answer 11

The principal argument of z, arg(z), is the angle θ measured in radians which -π< θ ≤π between the line connecting the origin, and the point z and the positive real axis