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123ryoma12

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Ok, so the question isn't the problem but rather the method used to get the answer.
This is the answer:
Capture.PNG
Why is it that we're allowed to take the modulus of both sides to get a locus because if I do the same with a fixed point for example:
z = 1 + i
|z| = sqrt(2)
x^2 + y^2 = 2
I get that locus, which is obviously wrong because z is a fixed point.
 

Paradoxica

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View attachment 33512
Ok, so the question isn't the problem but rather the method used to get the answer.
This is the answer:
View attachment 33513
Why is it that we're allowed to take the modulus of both sides to get a locus because if I do the same with a fixed point for example:
z = 1 + i
|z| = sqrt(2)
x^2 + y^2 = 2
I get that locus, which is obviously wrong because z is a fixed point.
Your "counterexample" doesn't work because there is no variable.

In the question you are flummoxing over, there are two variables, and you are given the behaviour of one.

The relation between the variables is given and you are asked to determine the behaviour of the dependent variable.
 

InteGrand

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View attachment 33512
Ok, so the question isn't the problem but rather the method used to get the answer.
This is the answer:
View attachment 33513
Why is it that we're allowed to take the modulus of both sides to get a locus because if I do the same with a fixed point for example:
z = 1 + i
|z| = sqrt(2)
x^2 + y^2 = 2
I get that locus, which is obviously wrong because z is a fixed point.
 
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