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.

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(52874) (Show Source): You can put this solution on YOUR website!

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The problem with representing with is that .

The best way to evaluate is to evaluate it directly:

.

BUT, in case you actually meant , then

RELATED QUESTIONS
What is (3i)^4 + 1 in standard form... (answered by jim_thompson5910)
What is (3i)^4 + 1 in standard form... (answered by DrBeeee)
Please help. I do not understand Write the complex number in rectangular form. 1.)... (answered by Edwin McCravy)
Express the product of 4-3i and 2+i in simplest a+bi form. Thank... (answered by jim_thompson5910)
This is my question, with 'i' being an imaginary number. The question is to express the... (answered by richard1234)
Express 4-3i/2+i in the form... (answered by mananth)
Simplify the following quotient of complex numbers into the form a + bi. (-4-3i)/(2-i) (answered by nyc_function)
Write the expression in the form a+bi 1. (8-3i) + (-6+2i) 2. {{{4/(2-i)}}}... (answered by stanbon)
hai i am doing B.Sc(maths) Ist year at madurai kamaraj university in correspondence. (answered by venugopalramana)