Modukus And Argument

Question 1

Mod

Answer 1

Distance from origin

So swaure root add sqaured

Question 2

Argument

Answer 2

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

Question 3

ALSO WHAT ARE THE LIMIRS FOR THE ARGUMENT,

Answer 3

CAN be -pi

Question 4

Arg(0)?

Answer 4

Undefined

Question 5

Complex conjudgste look conjugate in mod arg form?d

Answer 5

Yh they do but have to use symmetric properties of graphs to identify

Question 6

Mod arg form

Answer 6

Mod (cos (arg) +isin(arg))

DONT FORGET I!!,

Question 7

Convert back?

Answer 7

Put in calc , his why importsnt to make sure if be,ow axis then -

Question 8

How to multiply two complexes, what will argument and mod be?

Answer 8

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

Question 9

Principle argument form?

Answer 9

All values (especially after multiplying )
Should be

-Pi

Question 10

To do transformation from one line to other

Answer 10

See which bigger divide, or multiply the complex numbers as vectors

And do according to arg and mod , check if it works

Question 11

How to show exact value of cos using division and mod and arg

Answer 11

Divide using rationalisation

Equate this to the new mod arg form of the number that’s divided

And divide you’ll find

Question 12

Loci circles

Answer 12

Mod Z = r is circle radius r centred 00
Mod z-x = r
Is circulr centred at x with radius r

Question 13

Inequalities?

Answer 13

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

Question 14

Make sure to check inequality sign first and then put it in, so you can show dotted vs soldi

Question 15

How to sketch circle

Answer 15

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

Question 16

Loci perpendicular bisect r

Answer 16

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

Question 17

Make sure to find midpoint fir finding loci of perpendicular bisected as better

Answer 17

Intercepts and midpoint too

Question 18

Remember dotted line solid and kess than still applies for perpendicular bisector

Question 19

IF DONT KNOW WHAT TO SHADE, WHAT TO DO?

Answer 19

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

Question 20

If equal to each other what to do
And leave in WHAT FORM

Answer 20

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

Question 21

Using some techniques find min arg, make sure to use tangents, and also tan etc

Question 22

MAKE SURE YOU KEAVE IN TERMS OF Z!

Answer 22

SO COMPLEX FORM

Question 23

Remember min djstance mod z or agr is from

Answer 23

The actual thing!
Draw it first

Then find
Using whatever technique

Question 24

How to do half lines?

Answer 24

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)

Question 25

Remember gradient if half line is

Answer 25

Tan theta (depends make sure correct theta)

And equation is subbing point in
Normally origin
Might be a transformed lohnt

Question 26

Make sure when drawing half lines

Answer 26

• 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!

Question 27

Don’t be scared if kinda consistent go with it