Modulus help, please :/
my teacher is really annoying and has rushed through a completely new concept with us in a few lessons, "covering" complex numbers and modulus and argument. I have managed to work out how to do most questions, but there's one that i can't get right... is there any chance someone could talk me through it step-by-step?
|z+4| = 3 |z|
|z+4| = 3 |z|
Original post by TeslaCoil
my teacher is really annoying and has rushed through a completely new concept with us in a few lessons, "covering" complex numbers and modulus and argument. I have managed to work out how to do most questions, but there's one that i can't get right... is there any chance someone could talk me through it step-by-step?
|z+4| = 3 |z|
|z+4| = 3 |z|
If you square both sides, it'll 'get rid ' sign. Eg 3 squared same as -3 squared
So (z+4) squared equals (3z)squared I think!
Original post by TeslaCoil
my teacher is really annoying and has rushed through a completely new concept with us in a few lessons, "covering" complex numbers and modulus and argument. I have managed to work out how to do most questions, but there's one that i can't get right... is there any chance someone could talk me through it step-by-step?
|z+4| = 3 |z|
|z+4| = 3 |z|
If you write it out as |x+iy+4|=3|x+iy|, then you have sqrt((x+4)^2+y^2)=3*sqrt(x^2+y^2). Square both sides and see where that gets you.
THe modulus function is a function that turns the number within the | | signs to a positive, therefore if y = |x| where x=-3, y=3. Equally if x=3 then y=3.
The issue arises when you have a function such as yours and you want to find a variable within the modulus function - that variable could be either positive or negative but because of the modulus sign you don't know which. To eliminate this problem you square both sides because x^2 is always a positive value. This transforms |z+4| = 3 |z| into (z+4)^2 = (3z)^2 (notice all positive).
From there you'd expand out both sides and solve normally for z.
The issue arises when you have a function such as yours and you want to find a variable within the modulus function - that variable could be either positive or negative but because of the modulus sign you don't know which. To eliminate this problem you square both sides because x^2 is always a positive value. This transforms |z+4| = 3 |z| into (z+4)^2 = (3z)^2 (notice all positive).
From there you'd expand out both sides and solve normally for z.
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