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#1
Aug2207, 07:46 AM

P: 9

1. The problem statement, all variables and given/known data
Given that Z is a complex number with condition Z1+Z+1=7 Illustrate Z on Argand Diagram and write out the equation of Locuz Z I attempted to figured out the equation of locus Z, Z1+Z+1=7 x+yi1+x+yi+1=7 [tex]\sqrt{}[(x1)^2+y^2][/tex] + [tex]\sqrt{}[(x+1)^2 + y^2][/tex] = 7 [tex]\sqr{}x^2 + 1  2x + y^2 + x^2 + 1 + 2x + y^2 = 49[/tex] [tex]\sqr{}2x^2 + 2y^2 = 47[/tex] it's not necessary the correct answer though... however, I can't figure how to illustrate the diagram! help! 


#2
Aug2207, 09:16 AM

P: 980

Assuming that your calculations are correct, that gives a circle of radius [tex]\sqrt{47/2}[/tex]. However, I don't think it is... Check your algebra carefully  squaring both sides doesn't mean get rid of square roots!
Another way to think about it is that the original equation says that the distance from a point on the locus to the points +1 and 1 add up to 7. This is the condition for an ellipse with its foci at 1 and 1! And an ellipse is only a circle if the foci coincide. 


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