find all solutions to the complex equation cos 5z iSolution

Solution

cos 5z = i

take arccos both sides, we have

arccos(cos5z)= arccos (i)

Now we know that cos function have a period of 2pi and also positive in 4th and 1st quadrant hence

5z = 2pi k - arccos (i) ,   2pi k + arccos (i) , where k belongs to Z

=> z = 1/5 (2pi k - arccos (i)) , 1/5 (2pi k + arccos (i) )