Past exam of the mathematical methods I course of the University of Oxford / 2017 / 1 / c

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- Solution c

Solution

From the exponential definition,

cos (i u) = cosh u

. Therefore

cos (2 i ln 2) = cosh (ln 4) = \frac{4 + 1/4}{2} = \frac{17}{8} .

A cosine of a nonreal argument need not lie between

- 1

and

1

; that bound applies to real arguments.

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