Core Pure - Argand Diagrams Flashcards
What are the axis’ on a diagram?
The vertical axis is the imaginary axis (Im)
The horizontal axis is the real axis (Re)
What are the different ways to represent the modulus of a complex number?
What is the principle argument?
This normally refers to the argument, a, of any complex number in the range of (-π,π)
What is the important thing to remember when calculating the argument?
Use the positive numbers when working it out then adjust your answer according to the graph shown below
Check the answer on your calculator
What is the modulus argument form of a complex number?
What are the 2 rules for fast multiplication for complex numbers?
What are the 2 rules for fast division for complex numbers?
What is generally the most important thing to remember when working out regions in the argand diagram?
What is the general equation of a circle in the Argand diagram and in cartesian form?
Cartesian form - (x-a)^2+(y-b)^2=r^2
What is the general form of a perpendicular bisector?
How can you find the cartesian form of an equation:
You square both sides
What is the general equation for a half line?
What are the 2 main points to keep in mind when drawing a half line?
Tanθ=the gradient
There is a small circle around the starting point as the half line doesn’t include that pount
Draw an example of a half line
How do you turn the equation of a half line (in an Argand diagram) into a cartesian equation?
You work out tanθ to get the gradient
You use the initial point of the half line and use y-y1=m(x-x1)
What is the minimum point/distance of something?
The closest point/distance to the origin
What is the min/max argument of a half line?
The smallest/largest angle that is formed
What do you need to remember when working out the maximum of the argument (with a circle)?
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
What have you learned about drawing graphs in an Argand diagram?
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)
