Further Maths

• What are the formulas for summation?


  N (sigma) r=1 1= n

  
• What is the cartesian equation of a circle?


  (x-a)^2+(y-b)^2=r^2
• What is the argument in the different quadrants of an Argand diagram?


  Quadrant 1: arctan (y/x)

  Quadrant 2: arctan (y/x) + pi

  Quadrant 3: arctan (y/x) -pi

  Quadrant 4: arctan (y/x)

  
• What is the modulus argument form?


  A way to express a complex number using its modulus and argument

  Z= modulus (cos(arg)+isin(arg))
• What does the modulus of a complex number show?


  The length of the line segment (the length of the distance from the point of the complex number to the origin)
• What does the argument of a complex number show?


  The angle between the positive real axis and the line segment that connects the origin to the complex number.
• What is the equation for a complex number?


  Z= x+iy
• How do you find the angle of rotation using a 2x2 matrix?


  Using the cos and sin matrix

  
• What do you need to make sure you check when finding the angle of rotation using a 2x2 matrix?


  Ensure that the angle fits and that it gives the number of the matrix. Cos and Sin graphs can have two solutions, remember to check both of them by drawing the cos and sin graphs.
• How do you use the determinant of a Matrix to find the area scale factor?


  The determinant of a matrix represents the area scale factor
• What matrix represents a reflection in the y-axis?


  Reflection in y-axis:

  
• What matrix represents a reflection in the x-axis?


  Reflection in the x-axis:

  
• What matrix represents the reflection y=x?


  Y=x:

  
• What matrix represents the reflection y=-x?


  Y=-x: