Modukus And Argument Flashcards
Mod
Distance from origin
So swaure root add sqaured
Argument
Angle from real axis in RADIANS
If above then anti-clockwise
If below then clockwise
Find bith using tan , but if below the angle is NEGATIVE
And if above positbe always
Don’t use negative in the tan then
And remember RADIANS! Not 90° BUT PI/2
ALSO WHAT ARE THE LIMIRS FOR THE ARGUMENT,
CAN be -pi
Arg(0)?
Undefined
Complex conjudgste look conjugate in mod arg form?d
Yh they do but have to use symmetric properties of graphs to identify
Mod arg form
Mod (cos (arg) +isin(arg))
DONT FORGET I!!,
Convert back?
Put in calc , his why importsnt to make sure if be,ow axis then -
How to multiply two complexes, what will argument and mod be?
The mod of a complex is the multiplier, add the two arguments together
So new mod is mod x mod , arg is arg + arg
Write in mod arg form etc
Principle argument form?
All values (especially after multiplying )
Should be
-Pi
To do transformation from one line to other
See which bigger divide, or multiply the complex numbers as vectors
And do according to arg and mod , check if it works
How to show exact value of cos using division and mod and arg
Divide using rationalisation
Equate this to the new mod arg form of the number that’s divided
And divide you’ll find
Loci circles
Mod Z = r is circle radius r centred 00
Mod z-x = r
Is circulr centred at x with radius r
Inequalities?
Remember dotted for less than , solid for = to
1) draw the circle out with radius, if it says less than then inside circle shade, if more then than it’s outside as this is greater than rafiud
Make sure to check inequality sign first and then put it in, so you can show dotted vs soldi
How to sketch circle
1) write down the centre
2) check if it goes through origin by seeing if radius = to min distance
Then you can find the x intercept this way
And y intercepted too
2) then dotted line
And then the shade
And then max min is easy
But make sure intercepts
Loci perpendicular bisect r
Kike the disstnce between two circles
Mod z +1 = mod z +2, is distance between -1 and -2
How to do?
Sub in x +iy for z and find the mod, x2 and y2 will cancel
Group them tigether and factor out I first
Make sure to find midpoint fir finding loci of perpendicular bisected as better
Intercepts and midpoint too
Remember dotted line solid and kess than still applies for perpendicular bisector
IF DONT KNOW WHAT TO SHADE, WHAT TO DO?
USE FULL EXPANSION, and then you have equation of line ,
Sub in points to see if it fits, as In put in two points not on the line, and see if inequality holds
That’s how you know
And make sure inequality legit
If equal to each other what to do
And leave in WHAT FORM
Have to find the exact values not just line
And re =0, means only in I’m, find Cartesian and make x 0
COMPLEX FORM
Using some techniques find min arg, make sure to use tangents, and also tan etc
MAKE SURE YOU KEAVE IN TERMS OF Z!
SO COMPLEX FORM
Remember min djstance mod z or agr is from
The actual thing!
Draw it first
Then find
Using whatever technique
How to do half lines?
This is using arguments, remember can never be (0,0), and Yh
And the equation of line is possible to find out using y = tan x, but like gotta make sure right angle (might have to do pi -et)
Remember gradient if half line is
Tan theta (depends make sure correct theta)
And equation is subbing point in
Normally origin
Might be a transformed lohnt
Make sure when drawing half lines
- that gradient checked fir positbe negative (just be wise negative arg don’t mean anything)
- thst circle drawn at starting
Domain stated
CHEKC y intercept to draw line otherwise it just a sketch!
Don’t be scared if kinda consistent go with it
