OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 1 / 1B / b / ii / Solution

The logarithms of

1 + ω = e^{iπ /3}

are

i (\frac{π}{3} + 2 πk), k \in Z .

The definition of complex exponentiation therefore gives all values as

exp [i (1 + ω) (\frac{π}{3} + 2 πk)] .

Since

1 + ω = \frac{1}{2} + i \frac{3}{2}

, these can be written

(- 1)^{k} e^{- 3 π (k + 1/6)} e^{iπ /6}, k \in Z .

Solved by gpt-5.6-sol high.

 Ancestors (12)