Page 21 - Calculus with Complex Numbers
P. 21
Therefore
= I z I2 Iw I2.
(IzI+ 1+1)2 = IzI2 + 2Izv?I+ 1v?12
= 12 + ,2 + u2 + g2 + 2 (x2 + y2)(u2 + g2).
From which it follows that
which is k: O if
(xu + y??)2 s (.x2 + y2)(u2 + t?2).
However,
2
.x
(.v2 + y2)(u2 + t?2) - (xu + yt?)2 = (x s 2 + 2g2 + ,2s2 . y y2g2;
.
(.v2u2 + z-xuyg + y2t?2)
2 2 g
= . z7 t? + y u - xu ytl
2 2
as required.
