Flashcards

Argard Diagrams

Doc Boff Further Maths AS level English 16 cards

Cards in this deck (16)

1What is the name given to the diagram which represents complex numbers?The Argard diagram
2On the Argard diagram, what name is given to the distance from the origin to the complex number?The Modulus (aka "mod z" or |z|)
3What is the name of the anticlockwise angle from the real positive axis to the modulus?The Argument (aka arg(z))
4What happens if the Argument is clockwise?The angle is negative
5Which therom is used to work out the Modulus?Pythagoras
6How to you work out the Argument?tan-1(o/a)
OR if obtuse it's easier to do:
180-(tan-1(o/a))
7Convert 180 degrees to radianspi
8Convert pi/6 to degrees180/6= 30 degrees
9What is Cartesian form?p+qi
10What equation can be used to find the Cartesian form from both the Modulus and Argument?z=r(cosx+isinx)
(r=mod , x (theta) = arg)
11How is modulus-argument form represented?(r,theta)
12What happens to the moduli and arguments when we multiply complex numbers?The moduli are are multiplied
The arguments are added
(|Z1Z2|) = |Z1|*|Z2|
arg(Z1Z2) = arg(Z1)+arg(Z2)
13What happens to the moduli and arguments when we divide complex numbers?The moduli are are divided
The arguments are subtracted
(|Z1/Z2|) = |Z1|/|Z2|
arg(Z1Z2) = arg(Z1)-arg(Z2)
14cos(theta) is also equal to what?cos(-theta)
15sin(-theta) is also equal to what?-sin(theta)
16cos(pi/6)-isin(pi/6) = ...cos(-pi/6) + isin(-pi/6)