SOLUTION: (1+i) to the 100th. I have a TI-89 that will solve this and the answer is -1.1259E15 but how was the solution derived?

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: (1+i) to the 100th. I have a TI-89 that will solve this and the answer is -1.1259E15 but how was the solution derived?      Log On


   

Question 464918: (1+i) to the 100th. I have a TI-89 that will solve this and the answer is -1.1259E15 but how was the solution derived?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
If we were to expand the whole thing,



We see that the real part is



and the imaginary part is



All of the imaginary terms cancel out, because we can group the terms together, noting that nCk = nC(n-k):



Hence, we are left with the real part, which happens to be that real number you posted.