24 



Ellery IV. Dcms 



A C- = (x/ + ix e " y- — k- + 2i (.iV + ix e " )kcos<f> 

 = x e ' 2 — in- -f- 2\X e 'k COS (f>. 



If the lines of real slope through A and C are drawn at right 

 angles B will be an element of a circle on AC as diameter. All 

 the elements gotten in this way will have their black points on a 

 circle of diameter x e ' and their blue points on a circle of diameter 

 T 



Fig. 24. 



n. Other elements are obtained by the intersection of lines of 

 imaginary slope passing through A and C. In particular, the 

 circular rays through A and C intersect in I and / and two other 

 points. The locus of all such points is, in general, a circle of 

 complex radius and complex center. 



Area 



The area of a triangle whose vertices are P 1} P«, P 3 is, coordi- 

 nates being rectangular, 



1, yu 1 



-i- 2 > y z > 1 



x s , y 3 , 1 



In case P 1> and P 2 are on the line y = mx-\-b this becomes 

 £ ( mx s -f b —y s ) (x 1 — x 2 ) . 



24 



