modulus of complex numbers Watch

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sarah12345
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#1
Report Thread starter 13 years ago
#1
im doint this question at the mo

a complex number z satisfies the equation |z-3-4i|=2

find the greatest value of |z|

i know that its a circle centre 3,4 radius 2 but i dont see how to work out when |z| is greatest

thanks alot
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SsEe
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Point on the circle furthest from the origin.
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sarah12345
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but how do i know which point that is?
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RichE
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(Original post by sarah12345)
but how do i know which point that is?
It's at 7/5 (3+4i) because that to the centre of the circle and following the radius on in the same direction
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SsEe
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Geometry. Line straight through the centre of the circle to the other side. You don't need the point's coordinates. Distance to centre + radius is the answer.
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sarah12345
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thanks sooo much

then how would i work out the difference between the greatest and least values of arg z?


thanks
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RichE
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(Original post by sarah12345)
thanks sooo much

then how would i work out the difference between the greatest and least values of arg z?


thanks
the least value will be 3 achieved at 3/5(3+4i) - i.e. at the other end of the diameter

So the difference is the length of a diameter - that is 4
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sarah12345
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(Original post by RichE)
the least value will be 3 achieved at 3/5(3+4i) - i.e. at the other end of the diameter

So the difference is the length of a diameter - that is 4
thanks but i meant find the difference in arg z?
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