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Let
. Let . Hint: Usea) Find the relation between x and y such that:
i)
b) In each case describe carefully the locus of z.
I don't know how to start, help please!
Last edited by Identity (2009-04-04 04:36:41)
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Modulus-argument form seems like the thing to use here.
Set z = r(cosθ + i sinθ).
Then z² = r²(cos(2θ) + i sin(2θ)), and you get a similar thing for z³.
That should let you find conditions on r and θ for the power of z being in S, and then you can get conditions on x and y by using those.
Why did the vector cross the road?
It wanted to be normal.
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Wait, so is this right for
? andIf
, andSo
But here
isn't any single value, rather it is within a range of values, how can you change this to x and y?Offline
That looks right, except that θ could also be in [9π/8,7π/6].
You can use the modulus part to say x²+y² = 3, and the arg part will give a restriction as well. I'd guess that's what you're meant to say.
Why did the vector cross the road?
It wanted to be normal.
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Thanks mathsy
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