Suppose and . If , then how are related? How are related?

If , then . Therefore, and since .

Is this correct?

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- Sep 4th 2010, 06:02 PMdwsmithZ_{1}=z_{2}
Suppose and . If , then how are related? How are related?

If , then . Therefore, and since .

Is this correct? - Sep 4th 2010, 06:06 PMAckbeet
I don't think your answer takes into account fully the ambiguities inherent in polar coordinates. You have negative radii possibilities, as well as changing the angle by certain well-defined amounts. How does this change your picture?

- Sep 4th 2010, 06:11 PMdwsmith
But by definition, iff. . Why can't I use that fact?

- Sep 4th 2010, 06:18 PMAckbeet
Sure, but that's cartesian coordinates. As soon as you start talking about radii and angles (i.e., polar coordinates), the game is different. Example:

In fact, in polar coordinates, the point is the same point as

So from this, you can see that setting

is simply not going to imply that and

Even if you throw in the other equation (the y equation), you're not going to resolve all the ambiguities.