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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2021

Paper 1

The circle is
$$
\boxed{|z-5i|=5}.
$$
The direction from its center $c=5i$ to $z_0=15/4$ is
$$
z_0-c=\frac{15}{4}-5i,
\qquad
|z_0-c|=\frac{25}{4},
$$
so the corresponding unit direction is $3/5-4i/5$. Moving a distance five from the center in the two directions gives
$$
z=5i\pm5\left(\frac35-\frac45i\right).
$$
Thus the intersections are
$$
\boxed{z=3+i\quad\text{and}\quad z=-3+9i}.
$$


Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 1 / 1C / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 1 / 1C / b / Solution

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Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 1 / 1C / b / Solution

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