Labels:graphics | graphic design | sketch | black and white | black | symbol OCR: Figure 12-20: Illustration of the Range of the Function \1 + z2 The graph of q(z) = \1 + z2 looks like that of p(z) = V1 - z2 except for the shading. You might not expect p and g to be related in the same way that cos and cosh are, but after a little reflection (or perhaps I should say, after turning it around in one's mind) one can see that q( is) = p(s). This formula is indeed of exactly the gamme form as cosh is = cos z. The function v 1 + z2 maps both halves of the real axis into [1, +00] on the real axia. The segmenta [U, {] and [0, - s] of the imaginary axis are each mapped backwards onto segment [0, 1] of the real axia; [$, +oos] and [ -, - pos] are each mapped onto the positive imaginary axis (but if minus zero is supported then opposite sides of the imaginary axis map to opposite halves of the imaginary axis-for example, y( +0 + 2%) = v5: but g(-0 +2%) = - v5:).
