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/
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Question 506736: This is my question, with 'i' being an imaginary number. The question is to express the complex numbers in simplified cartesian form.
( + )^39 x ()^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) (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,
(\frac{4}{5} + \frac{3i}{5}) = e^{i \theta}e^{i(\pi - \theta)} = e^{i \pi} = -1)
What we want is this number raised to the 39th power. Since (-1)^39 = -1, the answer is -1 (or -1 + 0i).
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