what-is-the-value-of-cos-1-i-and-cos-1-i-

Question Number 35231 by abdo.msup.com last updated on 17/May/18

w h a t i s t h e v a l u e o f c o s (1 + i) a n d

c o s (1 - i) ?

Commented by abdo mathsup 649 cc last updated on 17/May/18

w e h a v e t h e f o r m u l a e s c o s (z) = c h (i z) a n d

s i n (z) = s h (i z) \Rightarrow c o s (1 + i) = c h (i (1 + i))

= c h (- 1 + i) = \frac{e^{- 1 + i} + e^{1 - i}}{2}

= \frac{1}{2} {e^{- 1} c o s (1) + {i e}^{- 1} s i n (1) + e c o s (1) - i e s i n (1)}

= \frac{1}{2} {(e + e^{- 1}) c o s (1) + i (e^{- 1} - e) s i n (1)}

c o s (1 - i) = c h (i + 1) = \frac{e^{1 + i} + e^{- 1 - i}}{2}

= \frac{1}{2} {e c o s (1) + i e s i n (1) + e^{- 1} c o s (1) - {i e}^{- 1} s i n (1)}

= \frac{1}{2} {(e + e^{- 1}) c o s (1) + i (e - e^{- 1}) s i n (1)}