Question

if sin (logii)= a+ib, find a and b, hence find cos (log ii)​

Answer 1

Answer:

Step-by-step explanation:

Given if sin (logi^i)= a+ib, find a and b, hence find cos (log i^i)​

Given sin log i^i = a + ib

We need to find a and b

exp(i log i) = i^i

exp(i logi) = exp(ilgogi(cos π/2 + isinπ/2)) = i^i

exp(ilog(e^iπ/2) = exp(i(iπ/2)

     logi^i = loge^-π/2

     logi^i = - π/2

sinlogi^i = sin(-π/2)

               = sin(-90)

               = - 1

 sin logi^i = - 1

a + ib = - 1

a = -1 and b = 0

Now cos(logi^i) = √1 – sin^2logi^i

                          = √1 – (-1)^2  

                           = √1 – 1

          Cos(logi^i) = 0