Argand Diagrams

Question 1

What are the axis’ on a diagram?

Answer 1

The vertical axis is the imaginary axis (Im)
The horizontal axis is the real axis (Re)

Question 2

What are the different ways to represent the modulus of a complex number?

Answer 2

Question 3

What is the principle argument?

Answer 3

This normally refers to the argument, a, of any complex number in the range of (-π,π)

Question 4

What is the important thing to remember when calculating the argument?

Answer 4

Use the positive numbers when working it out then adjust your answer according to the graph shown below

Check the answer on your calculator

Question 5

What is the modulus argument form of a complex number?

Answer 5

Question 6

What are the 2 rules for fast multiplication for complex numbers?

Answer 6

Question 7

What are the 2 rules for fast division for complex numbers?

Answer 7

Question 8

What is generally the most important thing to remember when working out regions in the argand diagram?

Answer 8

Question 9

What is the general equation of a circle in the Argand diagram and in cartesian form?

Answer 9

Cartesian form - (x-a)^2+(y-b)^2=r^2

Question 10

What is the general form of a perpendicular bisector?

Answer 10

Question 11

How can you find the cartesian form of an equation:

Answer 11

You square both sides

Question 12

What is the general equation for a half line?

Answer 12

Question 13

What are the 2 main points to keep in mind when drawing a half line?

Answer 13

Tanθ=the gradient

There is a small circle around the starting point as the half line doesn’t include that pount

Question 14

Draw an example of a half line

Answer 14

Question 15

How do you turn the equation of a half line (in an Argand diagram) into a cartesian equation?

Answer 15

You work out tanθ to get the gradient
You use the initial point of the half line and use y-y1=m(x-x1)

Question 16

What is the minimum point/distance of something?

Answer 16

The closest point/distance to the origin

Question 17

What is the min/max argument of a half line?

Answer 17

The smallest/largest angle that is formed

Question 18

What do you need to remember when working out the maximum of the argument (with a circle)?

Answer 18

The max angle will be formed at the tangent to the circle and that might not necessarily be at the exact maximum point on the circle

Question 19

What have you learned about drawing graphs in an Argand diagram?

Answer 19

Complex numbers are like vectors - when drawing a point in an argand diagram you need to draw a line connecting the point to the origin with an arrow (like a vector)

When drawing a circle make sure to include a line representing a radius

You only need the radius and the center labeled and that it (check)