Trigonometric Complex Numbers with example

Introduction:
                   In mathematics, the trigonometric functions are also called as circular functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are the most important in the study of triangles and modeling periodic phenomena, among many other applications. Now let us discuss about the trigonometric complex numbers.

Problems on Trigonometric Complex Numbers:

Complex trigonometric functions
 Through Euler's formula we know that
 e^ix = Cos x + i Sin x   and hence, e^-ix = Cos x - i Sin x
 This gives us the two identities:
 Cos x = ½(e^ix + e^-ix)   and Sin x = ½(e^ix - e-^ix)
             Then complex trigonometric functions can be defined by analogy as: Cos z = ½(eiz + e-iz)  and Sin z = ½(eiz - e-iz);  while other complex trigonometric functions
1. Find Trigonometry complex   ( 3 + 5i) - (8 +3i)
Answer:          
               =(3 + 5i) - (8+ 3i)
               =(3 - 8) + (5i - 3i)
               =-5 + 2i

2. Solve the trigonometry complex triangle function of the sides a=8, b=5 and c=4 of the trigonometry area triangle
Solution:
             Trigonometry function of s= (`1/2` ) (a+b+c) =8.5
                Function area =√ [s(s-a) (s-b) (s-c)] = 9.045
Hope you liked the above explanation. Please leave your comments, if you have any doubts.