SOLUTION: This is my question, with 'i' being an imaginary number. The question is to express the complex numbers in simplified cartesian form. ({{{3/5}}} + {{{4i/5}}})^39 x ({{{3i/5 + 4/

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: This is my question, with 'i' being an imaginary number. The question is to express the complex numbers in simplified cartesian form. ({{{3/5}}} + {{{4i/5}}})^39 x ({{{3i/5 + 4/      Log On


   

Question 506736: This is my question, with 'i' being an imaginary number. The question is to express the complex numbers in simplified cartesian form.
(3%2F5 + 4i%2F5)^39 x (3i%2F5+%2B+4%2F5)^39
I have tried finding the modulus, and that gives me the square root of (3/5)^2 + (4/5)^2, which equals 1. I don't know where to go from there, or if I've made a mistake already.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Note that

where theta is the arc-cosine of 3/5. Then,



because the arguments of both complex numbers are complementary angles. Then,



What we want is this number raised to the 39th power. Since (-1)^39 = -1, the answer is -1 (or -1 + 0i).