Clarification

[lisafaustina]

1. Linear dependence in vectors - if there are vector a,b and c is it always a=b+c or..? Very confused on this one.

2. Does Arg(z1)-Arg(z2) = Arg(z1/z2)?

[98.40_for_sure]

1. VCAA noted in an assessment report that linear dependence is NOT a+b+c=0. They want you to know that it is ma+nb+pc=0, or c=ma+nb. I think they said something about using the latter since 2 variables is neater than 3.

2. Lets take a simple case.
Let z1=1+i, z2=1-i
Arg(z1) = pi/4, Arg(z2) = -pi/4
So pi/4 - (-pi/4) = pi/2

Now let's try the right hand side
Arg(z1/z2) = Arg(i) = pi/2

So yes, the rule is true.

[jasoN-]

Moreso in general:



as not always the addition/subtraction of Arg(z)s will yield a result in the domain of Arg(z)