Princess Sophie E: In an argand diagram, P represents the complex number such that {Z:3|Z+3|=|Z+4i|}
show that P lies on the circle and find
a)the radius of the circle
b)the complex numbers represented by the centre.
Hey Princess Sophie E!
If we write Z=x+iy, we can rewrite the expression to:
3| (x+3) + iy | = | x + i(y+4) |
9 ( (x+3)
2 + y
2 ) = x
2 + (y+4)
2 8x
2 + 54x + 8y
2 - 8y + 65 = 0
x
2 + (27/4)x + y
2 - y + 65/8 = 0
Complete the squares
(x + 27/8)
2 - (27/8)
2 + (y - 1/2)
2 - (1/2)
2 + 65/8 = 0
(x + 27/8)
2 + (y - 1/2)
2 = (15/8)
2 Can I assume you can verify if this represents a circle and also that you read off the radius and the center?
Cheers!
+72 
+135 
