Paper 1, Section I, C

(a) Find all complex solutions to the equation $z^{i}=1$.

(b) Write down an equation for the numbers $z$ which describe, in the complex plane, a circle with radius 5 centred at $c=5 i$. Find the points on the circle at which it intersects the line passing through $c$ and $z_{0}=\frac{15}{4}$.

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