Maths P3 help!!

[Hello111]

I got problems in two topics.

First one is with solving equations and inequalities having modulus in them.
For example |x – a| < b ⇔ a – b < x < a + b
So what are the solutions of other equations and inequalities?
|x – a| > b
|x – a| > |b|
|x – a| > |b - c|
|x – a|^2 > b^2
|x – a|^2 > |b|^2
(x – a)^2 > b^2
And anything I missed.

Also I got problems with argand diagrams.
How do you draw stuffs like |z – a|< k, |z – a|= |z – b|, arg(z – a) = α.
Also it would be awesome if you could help me draw some other of the notations of complex numbers.

 

[ahmed t]

square both sides and solve as a quadratic equation
but remember chek ur ansers with the original equation after u finish
u may do it a graphical way but it is way too time consuming

 

[Hello111]

Will squaring both sides always work in every kind of inequalities involving modulus, given that I check my answer?

 

[ahmed t]

yes it always will
remember u will get a quadratice inequality so remeber the purpose of >,<
as for|z – a|< k it means a a circle with center a and radius k
and for |z – a|= |z – b| it means the perpendicular bisector of the line between point a and point b
arg(z – a) = α this means u draw a horizontal line at the point a and draw an angle of αfrom that point