SOLUTION: Express "(1 + 3i)^-4" in the form a + bi. What I have tried already is to, convert the "1 + 3i" into polar form, which is (2e^(pi/3))^-4. I'm not sure what to do from there though.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Express "(1 + 3i)^-4" in the form a + bi. What I have tried already is to, convert the "1 + 3i" into polar form, which is (2e^(pi/3))^-4. I'm not sure what to do from there though.      Log On


   

Question 1184507: Express "(1 + 3i)^-4" in the form a + bi. What I have tried already is to, convert the "1 + 3i" into polar form, which is (2e^(pi/3))^-4. I'm not sure what to do from there though. Any help is appreciated, and thanks.
Found 2 solutions by ikleyn, robertb:
Answer by ikleyn(52870) About Me  (Show Source):
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The problem with representing %281%2B3i%29%5E%28-4%29 with %282e%5E%28%28pi%2F3%29%2Ai%29%29%5E%28-4%29 is that 1%2B3i+%3C%3E+2e%5E%28%28pi%2F3%29%2Ai%29+=+1%2B+sqrt%283%29%2Ai.

The best way to evaluate %281%2B3i%29%5E%28-4%29 is to evaluate it directly:

.

BUT, in case you actually meant %281%2Bsqrt%283%29i%29%5E%28-4%29, then