COMPLEX ANALYSIS Function Values Find in the form u iv COMP

COMPLEX ANALYSIS

Function Values. Find, in the form u + iv.

COMPLEX ANALYSIS Function Values. Find, in the form u + iv. Cos (5 + i)

Solution

cos(5 + i)

USing cos(a+b) = cosacosb - sinasinb, we get :

cos5cosi - sin5sini

cos5 and sin5 from the calculator

cos(i) = (e^(i^2) + e^(-i^2)) / 2e ---> (1 + e^2)/2e = 1.5430806

sin(i) = ((e^2 - 1)/(2e)) * i = 1.1752012i

cos5cosi - sin5sini

0.28366 * 1.5430806 - -0.95892 * 1.1752012i

0.43771 + 1.12692i ---> ANSWER