 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/9/a/iv/solution

For the positive real base ten, use its real natural logarithm. Then Euler's formula gives

1 0^{i} = e^{i l n 10} = cos (ln 10) + i sin (ln 10) .

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