In Example it was shown that the image of a vertical line x = k, k ≠ 0, under w = z2 is th...

In Example it was shown that the image of a vertical line x = k, k ≠ 0, under w = z2 is the parabola . Use this result, your knowledge of linear mappings, and the fact that w = −(iz)2 to prove that the image of a horizontal line y = k, k ≠ 0, is the parabola .

EXAMPLE Image of a Vertical Line under w = z 2

FIGURE 2.4.4 The mapping w = z2

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