The Imaginary m Geometry 



33 



from the figure 



cos 6 = cos 6' ch 0" — i sin 9 sh 0', 

 sin = sin 0' ch 6" -f t cos sh ^, 

 tanfl' + ithfl" 



tan# = 



i — i tan ^ th 6" 



Note that tan -1 / = i th -1 I ==* oo the imaginary part of the angle 

 that the /-ray makes with .r-axis. Note also that 



tair 1 ki = tr/2 -J- tan -1 i/k. 

 // 



/ ' \ Hot6.tior>. 



/ / \ lmAjin»rc( Area .... I' ,.';.! 



/ / \ TCi&l Area . 



'! \ 



—H - \ 



M/<SIV P 



3in9 



