SOLUTION: z is the complex number 1+i, where i^2=-1. (i) Find z^2 and z^3. (ii) Verify that z^4=-4.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: z is the complex number 1+i, where i^2=-1. (i) Find z^2 and z^3. (ii) Verify that z^4=-4.      Log On


   

Question 938813: z is the complex number 1+i, where i^2=-1.
(i) Find z^2 and z^3.
(ii) Verify that z^4=-4.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
z = 1+i
...
(1+i)^2 = 1 + 2i - 1 = 2i
z^4 = (2i)^2 = -4
...
z^3 = 2i(1+i) = 2i - 2