How to find the exponential of ?

Z=(1+i)^100

1 Answer
Oct 15, 2017

Use the form

#Z = (a+bi)^n = (sqrt(a^2+b^2))^n e^(i(ntan^-1(b/a)))#

Explanation:

Substitute, #a = 1#, #b = 1#, and #n = 100#

#Z = (1+1i)^100 = (sqrt(1^2+1^2))^100 e^(i(100tan^-1(1/1)))#

#Z = (1+1i)^100 = 2^50 e^(i(25pi)#

#Z = (1+1i)^100 = -2^50#