Past exam of the mathematics course of the University of Cambridge / 2018 / ia / Paper 1 / 1C / iv

Table of contents
- Solution iv

Solution

The base

e^{5 iπ /2}

is the complex number

i

. Principal exponentiation uses the principal logarithm of that base, so this is the same equation as in part iii:

z = \frac{1}{3} + 4 k - \frac{2 i lo g 2}{π}, k \in Z .

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