 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/10/b/i/solution

u = X + iY

gives

X = 2 x

Y = y

. Substitute

x = X /2

y = Y

\frac{( X + 2 ) ^{2}}{1 6 ^{2}} + \frac{( Y + 1 ) ^{2}}{8 ^{2}} = 1,

centered at

(- 2, - 1)

with horizontal semiaxis sixteen and vertical semiaxis eight. The map covers the whole ellipse as

z

covers the circle.

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