 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2017/1/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.

 New to topics? Read the docs here!