Core Pure - Argand Diagrams Flashcards

1
Q

What are the axis’ on a diagram?

A

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

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2
Q

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

A
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3
Q

What is the principle argument?

A

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

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4
Q

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

A

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

Check the answer on your calculator

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5
Q

What is the modulus argument form of a complex number?

A
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6
Q

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

A
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7
Q

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

A
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8
Q

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

A
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9
Q

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

A

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

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10
Q

What is the general form of a perpendicular bisector?

A
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11
Q

How can you find the cartesian form of an equation:

A

You square both sides

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12
Q

What is the general equation for a half line?

A
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13
Q

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

A

Tanθ=the gradient

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

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14
Q

Draw an example of a half line

A
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15
Q

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

A

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

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16
Q

What is the minimum point/distance of something?

A

The closest point/distance to the origin

17
Q

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

A

The smallest/largest angle that is formed

18
Q

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

A

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

19
Q

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

A

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)