Chapter 2- Argand Diagrams

Question 1

What is the modulus or absolute value of a complex number?

Answer 1

The distance from the origin to that number on an argand diagram (use pythagoras)

Question 2

What is the argument of a complex number?

Answer 2

The angle between the positive real axis and line from the origin to the number on the argand diagram measured anticlockwise

Question 3

What is the modulus argument form of a complex number?

Answer 3

z = r(cosθ + i sinθ)
-r is the modulus and θ is the argument

Question 4

What is the rule for finding the new modulus when multiplying complex numbers?

Answer 4

Moduli are multiplied together

Question 5

What is the rule for finding the argument when multiplying two complex numbers?

Answer 5

Add the arguments to each other

Question 6

What is the rule for finding the new modulus when dividing complex numbers?

Answer 6

Moduli are divided

Question 7

What is the rule for finding the argument when dividing complex numbers?

Answer 7

Subtract the argument from each other

Question 8

What does a, b and C represent in |z- (a+ bi)|= C

Answer 8

Will be a circle of radius C (distance from point)
Centre of (a,b)

Question 9

What does |z-z1| = |z-z2| show?

Answer 9

The perpendicular bisector of the line joining z1 and z2

Question 10

What does |z - 4| < |z - 6| mean?

Answer 10

Represents the region x < 5